Maths-
General
Easy
Question
Given: P(0,h), Q(h,0), R(-h,0)
Prove: △ PQR is an isosceles triangle.
Hint:
Use distance formula.
The correct answer is: PQR is an isosceles triangle.
Complete step by step solution:
Here P = (0,h)
Q = (h,0)
R = (-h,0)
Length PQ = ![square root of left parenthesis 0 minus h right parenthesis squared plus left parenthesis h minus 0 right parenthesis squared end root equals square root of 2 h squared end root](data:image/png;base64,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)
Length PR = ![square root of left parenthesis 0 minus h right parenthesis squared plus left parenthesis negative h minus 0 right parenthesis squared end root equals square root of 2 h squared end root](data:image/png;base64,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)
Length QR = ![square root of open parentheses 0 minus 0 plus left parenthesis negative h minus h right parenthesis squared close end root equals square root of 4 h squared end root equals 2 h](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP0AAAAYCAYAAAAxvPvNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAABIpJREFUeNrtW11IFUEUHuIiIpcwFCwKFLmE9CBCSZlFRCESEhH0IPVgKCEh0UPQQ0FBD0lBRg9BZPhWIBFBYoGIhYhYEFH0Qz32UL4YaJTcfm7n4BEu2+zu7O7Z2bl354MPrrPrnjlnzsyemXNWCAuL8kIlsGAILSwsNKAT+MKaofxWUMvSok4MAS/b6cqDQ8BZawYLw/EeuMOagQcjwDPWDBYGowH4DZjRIGs1iskDZ4C5cjMmGvELsMn6VephsrMPAO9plrkGeBL4stwGej/wjcd1VHowJU6fFl0HSddScvZHwJ6EZC+XmwNcBV50udacor1+mnQV9CZvLhFnx2h0Cbg+Adl7gM/KbfA/A1s8HMN5bS3wJnCOeIva4oBOWTMedoiKH/T21AUVeVuB0yXi7EFSdV3CO6sQZCw2kF80xqhbO/A+cJG2Va+AR+P0pW3AT0J+ONJCCjsxCTzoMPJkTAbRJctNVw7gvvi1xgkSRN40Tf4knD1oNHpJ4b4s8J3HpA9im83AMbJFnMCFtZv6jthCtu+Oy5cwrB9yuXaFDk+KcQR4Q3LvdZdORgGHLNU8skxXLmA6VOcBVBB5pyRnGLqcPQgwVbdL4T6MBHs9xl3VNqj7eIxRpR/qXSY3iy95GfMJcLejDcOQDsm9e+kaJzhkqU56ma5cuAA8C6wBXgPOAxdowiUtr80ROSXt7DI0CLVUXXuRLoWItkEbJJ3NWo7Dl3I+xsQ9RoWjbUHSJqhtnllpDlmqk37RRRYHRmmwpmmrgvuxjTSoVQnLqyDdOZ09ShVfraStX+HtVkFvxnqfcVe1TZjKQ87qxTaX7WYgX8pKHoDFOLc9BP9WbFtFntl5OWQVGGRFxUcKl7OSRa3GAHn5iM7OdQ4xQvJaHddUUnWDju1ZwZCxCAMsiZ+jyCVU/4uN6QzjMT3VxTjpl5lXQFNkRXkursTfJaswRlc/DJGXN8DRz5OffqWtVvEEwGjUK1XXLHkrFhjHQifWAR+6bGuV+79qTDTc86L2TdRWHTDknXcJgytjCO85ZCUd3m8X8mwDhm9TBshzhvcciBLmngb+pDFG+BWOCXor5hTGPe6xiBreN9KEz3H5ElZX/QXW0d8qJY0TkhADD9A6Jfd2xHSQF1WW6qSfcAmnoqKbFl3Vdt3y2kR86daw+AXso99ehWOqky2psQiCJtpqV3H7EoYAd+n3Y+Axn47I0liHXc4BRgR/yo5DVtIpO0w5Hndp7zVA3gDpbhKeAt/S77Bf1RUMGAtV4It4VPhnJ0L1f5hCJzwhXfIJ7RFuBStTFIZlKDw8J+Kr3IoqS3XSx1Wc8wB4IEC7bnluxTlJYh/wD3CnWPkQLMM06XWPhSrGhFrGJFT/q8mY4/SmV8Gs+L8+Gw8b7oiVwzSMHrAgIhvjwYYuWTJdo2KhaH+q0q5Tnl8ZbpLA86YPInwhSsGAseA4C2Dp/zQ9rF+xQ/aDm/KFygc3SWGY/LRHWERGKxmzNsD/4AKRlk9r06Ir7uNPGNy/uhB+auGBPmsCixJZgC0sLFKEjDVBcPwDXoRWAJwYky4AAAF4dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zcXJ0PjxtZmVuY2VkIGNsb3NlPSIiIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4wPC9tbj48bW8+JiN4MjIxMjs8L21vPjxtbj4wPC9tbj48bW8+KzwvbW8+PG1vPig8L21vPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmg8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmg8L21pPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PC9tc3FydD48bW8+PTwvbW8+PG1zcXJ0Pjxtbj40PC9tbj48bXN1cD48bWk+aDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21zcXJ0Pjxtbz49PC9tbz48bW4+MjwvbW4+PG1pPmg8L21pPjwvbWF0aD7ARPn2AAAAAElFTkSuQmCC)
Here length of PQ = PR
⇒PQR is an isosceles triangle.
Related Questions to study
Maths-
A rectangle with side lengths 3h and k has a vertex at (2h, k). Which point cannot be a vertex of the rectangle?
A rectangle with side lengths 3h and k has a vertex at (2h, k). Which point cannot be a vertex of the rectangle?
Maths-General
Maths-
Use △ ABC, where M, N, Q are midpoints of the sides.
MQ = 3y − 5, AC = 4y + 2
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPgAAADPCAYAAADYrhweAAAgAElEQVR4nO2deXhURbr/P3VOL9nYlwAiICAERXZUHFGQVVFZJIYlEBJgRMQ7V38zc2fmzuI8z733uePMOCN6WZQkZCMBDYgssg6rQRRZBAFRUBZF2SF7us+p3x/d59ABRFCgl9THp01IdzrnVNe33veteustIaWUKBSKiEQL9gUoFIqbhxK4QhHBKIErFBGMErhCEcEogSsUEYwSuEIRwSiBKxQRjBK4QhHBKIErFBGMErhCEcEogSsUEYwj2BegCCaB2xBE0K5CcfNQAo8QJCCQfsmKi/8P0LCUEgSYUiDxIrQq/wtcaNKJUBqPOJTAIwjT//WKOpWA9GAaGlI4MIRAwwsYCBz+AUIRaSiBRxRXkagw8XjLKS4uo7RMUL9hA9zR0YAX31SMiZqSiTzUJxqxSMAEYfgfcPbMt/z8mTQeeaQv23fswoETcPteLgyqx+SKSEAJPIKQEqT1n5RIaeL1ejAMD2Cwb+8+Tp48Se06MXy0dTslZRIpNUxDIqVhR/CKyEEJPNKQ2IbYJ3ID0/RQVV7ChvVb6dq5J+OSx7Bm7XscP/6Nz6kXgJQqBo9AlMAjDkumJgiJpoGuS86cPc2Wol30/tkAHunfh6Nff87u3Tt9L5UaoCn7HYEogUcSwnLQfZimCUgEgs/2fwbSycMP96PdnXfSIeFOPtj6PlWVXiQCEw01jx55KIFHCJY0pQApfH66MExMj4FZZTI/N5827VrgMSs5f6aEnl3vZf2aNZw5fQqJwJAOlMAjD6GqqkYOBhITEwHoUiJNL0jJwQOf8eTjQ4mt15DYWnUQmFRVVnDw4Jf89//+hfGpEzClxK0JJfEIQ62DRyhSgGlKHE4nGzdswh3l5o033yAmNg4hJbou+N3vfsfq1at4eswY3C5XsC9ZcRNQLnqEIP3/F/g+VCFBaDplJaWsXLOGvv0G0rVbd9q3b0/7hHa0vbM9w4YPY8f27ezdtw+hekJEoj7WCMEStuZfJ5NCoOkODn11GGdULBMmTsJrGpjSRJoGyCr69XuEe+7pyOcHDijXPEJRMXgEIf1RuA9fAktJaSkXzpfQtGk8QhcIIdGkiUBiSPjm+Ek0l5uGDRriUjF4xKEEHkFcJnBTICUITcPrNXA4BQLDJ3Ahqaryojmi8Ph/JcrhUAKPMNQkW8QgubglzL+mLaVvjdsw7JcIIfzPCZxONx7DxKE5UHtFIxNlwSMK66O8KFZ5yT5QcVm+mrjCbykiBSVwhSKCUbPoCkUEo2LwGoRpmkgpEUIgpUTTNH9MrohUlMBrGFJKTNNUwq4hKBe9BuHbXXYRJfLIRwm8BnHo0CFWr16Nw+FA1/VgX47iFqBc9AjGirmllFRVVTFr1iy2b99O69atad++vR2PKyIXZcEjHEvEX3zxBQUFBRQVFVFQUEBFRYUSdw1ACTyCMU0T0zTxeDy89NJL1KlTh4EDB7J48WL27dsX7MtT3AKUwCMcl8vFkiVL2LRpEy+++CJ//OMfqaioIDc3l4qKCsB/4okiIlECjyCseNt6OBwOTp48SUZGBm3btuWpp56ie/fujBs3jvnz57NlyxYADMPAMAwl9AhECTyCEEJUe5imyfz58/n000/59a9/Td26ddF1nWHDhtG0aVPS09O5cOECoKx4pKIEHkFYMbcl1oMHD5KTk8ODDz5I//79kVLi9Xpp164dqamprF27liVLlqiMtghGCTzCsIRaVVVFQUEBJ0+eJC0tjbi4OIQQGIaBaZokJydz1113MWfOHM6ePVtN4MqaRw5K4BGGlYa6Y8cO8vPzGTFiBA888ICdxeZ2u3E4HNSuXZtp06Zx4MABMjMzbctvDQCGtYdcEdYogUcQVuxdXl7OwoULMU2TpKQkYmJiqrnh1tdBgwbRv39/cnJy2LdvH5qmqeSXCEMJPIKwdoht3LiR3NxcxowZQ8eOHe1Z9Utxu91MmjSJCxcuUFhYiMfjsXeaKZFHBkrgYc6l4i0vL2fWrFk0a9aMsWPHEh0dXW2b6KV069aNpKQk8vPzef/999F13d5xpgh/lMDDGEuIgevY77zzDh999BETJkygTZs2AGiahqZd/lGbpklsbCwpKSnExMSQl5dHSUmJmmSLIJTAw5jAmFrTNL755htee+01unbtyoQJE6q97vtcbiklrVq14umnn2bJkiVs3boVh8OhXPQIQQk8jLHcc8uKL1iwgEOHDjF58mRiY2Ov6mZbLrtpmkRFRZGUlETHjh157bXXOHXq1BUtviL8UJ9iGGNZZl3X+fTTT8nJyWHgwIH06dPnmqq2WAI3TZPWrVszZswYPvroIzZt2mRPtil3PbxRAg9jLAEahsH8+fMpKSnhueeeIy4u7gcFbg0MTqfTLv4wdOhQunXrxt/+9jeOHDliZ75Za+OK8EMJPIyxNpRs3ryZwsJCEhMT6dixoy3u67G+pmnSoEEDpk2bxldffUVeXh5QPb9dEX4ogYcxmqZx/vx5MjIyiI6OJjk5mdjY2Go7yq4Vy13v3bs3gwYNYv78+ezatctOflGueniiBB5GWBNq1gPg448/ZvXq1YwdO5b27dvb1vvHbCCRUuJ2u3nhhReorKwkIyMDr9errHcYowQeRlhutyXu48eP8/LLL3PPPfeQmJiIw+FA0zT7648RuJSShIQEnnrqKZYtW8aWLVvUbrMwRgk8jLCEbQlxxYoV7Ny5kwkTJtCqVaufNBFmueBCCBwOB2PHjqV+/fq8+eabXLhwQQk8TFECDyMskWmaxtGjR3njjTe47777GDJkyE+OkQOLRAC0b9+eKVOmsG7dOlavXv2Tr10RHJTAwxApJZmZmXz77bdMmzaNunXr/uTTSqy43cpi0zSNxx57jLvvvps5c+Zw/Phxe0nO6/WqSbcwQQk8zNB1nf3797No0SIGDx5M7969MQzjhrjQly6JNW3alMmTJ7N7927efvttW9jKXQ8flMDDCCEElZWVTJ8+naqqKiZNmkRUVBRw+a6yn4q1A23QoEHce++9ZGdnc/z4cTRNw+v1qsSXMEEJPEywxLtp0ybee+89kpOT6dq1602thlpZWUmtWrWYPHkyZ86cIT09ncrKyu/dnaYIPdSnFOIE7uU+d+4cWVlZxMfHM3LkSMA34abr+g3PNhNC4HK5MAyDfv36MWzYMLKzs9mzZ499XYrQRwk8hLm08MLixYtZu3Yt06ZNo23btsDFuPlGr1UHxuMul4vRo0fjdrtJT0+nqqpKxeFhghJ4CBNolb/++mtyc3Pp2LEjgwcPtiuv3Iq/L6WkU6dOpKSksGLFCv71r38pFz1MUJ9SCBN4Mqh1nlhaWhpNmjS56S5yYDqsYRg4HA6Sk5OpX78++fn5ykUPE5TAQxxd1zl69Cjp6ekMHjyY4cOHA99fhulGYb2/FeMDNGvWjGnTprFu3ToyMzMB8Hq9VFVVKcGHKErgIYwQAo/HQ25uLufPn2fUqFG43W77uZsdB19aEgrgySefpHv37mRlZXH06FE7MUbF5KGJEniIs2PHDubOncuwYcPo3bt30K7DKgtVp04dJk6cyKFDh1i0aBFVVVW2hVeEHkrgIUhg0kp6ejoul4tx48bZ1jtY6LqOw+FgwIABDBkyhDfffJO9e/eq8k4hjBJ4iGHlegshWLp0KStWrGDixIl06NAhqDnggevtcXFxTJgwgbKyMhYsWEBlZaXtogdOzimCjxJ4iGEYBrquc+rUKWbOnEnTpk1JTU0NuT3Z3bt3Z8SIEeTn5/PJJ59Ui8OVJQ8dlMBDDMtKLl26lG3btjF16lTq1Klju8ChInKXy0VqaiqNGjXi1Vdfpaqqyr6+ULlGhRJ4SBBYQ03XdQ4ePEhmZiYPPvggTzzxBE6nEyCkkktM06RDhw4kJiayceNGNm7ceNnhhorgEzo9poZixaxWaWKPx8OyZcs4fPgwU6ZMoX79+miahtPpDCmBg+/aR40aRatWrfiv//ovTp06BXBTN8Aoro/Q6jE1FCu+FkLw6aefkpmZyWOPPUbPnj2DfWnfiyXg5s2b8/zzz7Nz504KCwuVFQ8xlMCDjFUmyTrXe968eVRWVpKSkkLdunVD0hIG1m+TUjJgwAD69etHVlYW+/btw+FwBPkKFRZK4EHG2jEmhGDXrl0sXryYoUOH2nu9QxErs82qmV6vXj1+85vfcPz4cebPn09VVRVwMfwIxUGqpqAEHmQssZSXl/OXv/yF2rVrk5KSgsPhCGlhWC64lcXWoUMHBg8ezNtvv11tz/iPOYRBceNQAg8ypmmi6zpr165l06ZNJCcn2wcYhBNxcXGMGzcOIQQ5OTkUFxdXS2FVMXlwUAIPEpZF03Wd7777jtdee40OHTrw9NNPh524wXc/PXr0ICkpiXfffddOfrGeUxY8OCiB32ICjx+yKCgoYPfu3bz00ks0bdoUXderlTAOB0zTxOVyMXLkSOLj4/nrX//KuXPnLqtKo7i1KIHfYi4V7IEDBygoKOCRRx7hgQcesF8TamveP4Ql5ISEBMaPH8/mzZtZuXJltRx2xa0nvHpRBGBZb03TqKioICsri1OnTpGWlobb7Q7ZmfMfQtd1+96GDRvG3XffzcyZMykuLlbiDiJK4LeYwDXkvXv3snDhQoYMGcIDDzxgCz8cCYyxGzZsyC9/+UsOHDjAG2+8oeLvIBKevSmMEUKg6zrFxcVkZ2cTFRXFmDFjiI6Oxul0hq0YrPsKPPbokUceITs7m7179wLY6bgqJr91KIHfYqwZ5a1bt7JgwQJGjRpFly5dqln2cCSwzLJ1D8888wwlJSXk5ORQWlpq59wrbh1K4LcYTdMoLS1lzpw53H777YwcORKXyxVxnV8IQY8ePRg7dixLlizhww8/xOl0hu0AFq4ogdtIwAQM/1ffd9L/Yyn9/8YAvPZrJKb/d63fv7qLLYRg4cKFbNiwgYkTJ9KmTRt791UkdX4pJdHR0SQlJeF2uyksLKSkpARN06oNZBKrXS9+538DkAYSabexidXq/s9F/lBrK4QM16DvJyHBNJFCIBGAxDA8CAwMTzmnT31HuRFNg9taEW2auE2TSqegQnfgMs8jK4o5ceI0MbHNqNugNrrmQAiJME2EdIImIECrVuwphODMmTOMHDmS6OhoFi5cSGxsrO+KIkjggfnnpmnyj3/8g1deeYXZs2czdOjQyyYTK0zA6wHjNCfOVWHgolnd+rh1LxVCx6wqpay4Ao87hjq16uAWAlPz4DA0TIeORrXmVgRQMy24vPyfQoDD4eKrLw8x9LER3NezN5u37ARdB11iCtCQCI+X9DcyaN26C3/649/xejSE0LhoxS9574BCDkIIsrKy+PLLL3n22WeJioqyrVmkiBuqx+NOp5PExETuvPNO0tPTOX369BXv1enUOHPya0YMHc6gQUPZvftTcDnRnQ7Kiov51S9+wcw35qA5BHZzoyz4D1EzBX4JAr/Lh4nX40VKjeZNmzHr9Vc5X15JlcNA0wRuWcWZr4+zad0HdOjQDsMLHo/0v8OVBRp4dtiePXvIzs5mwIABPProoxFltQMJTFH1er20atWKlJQUPvroI9auXXvZ6zUkmjQwvFXExMZwvvgC8/Lnc+58MRId05B4vSa67kAVaL4+lMABhLgoTynBdDFixEgO7N3D7v378WgOvBKEt5QtGzai4WLwoEdBar6H/T6AkNW0bmV4VVZWMn/+fCoqKkhNTcXtdteo+mVJSUn07t2bv/71r3z99ddIKTEMA8MwEFIihIkwvDSoX4eBgwezZetWPij6ABMQmi+Msr16a0xV/CBK4H6E5ovkdF2jyoTOXbrSvnVLVq9ahRcdYZp4y0p5d+l73Hv/A9SpWwdTmggR4CRKruip67rO5s2beeeddxg9ejTdunWz14IjdQrEWhe3ij/UqlWL1NRUDh06RF5eni1unxeDPTgapkGfvg/RuUsnCgrmcfrcaTRNgCYwqq2fC19cpbgqSuBXwNSgdu26jHrqSYrWr+HLr44R5dD4fP9nfHOmhAFPPophlKEJL6b0Ul3V1TudEILS0lLy8vJwuVwkJycTExMTse65ReC9Wda6b9++9O/fn+zsbD755BNcLpfPw/H9BlLX8JgGderUJnX8GHZ+/BEb1q1DYiKQvgITKF1fD0rglyABj1kFuk7Pbl0wyov5qOgjNDxMf20GXXo/RKv2rRGaF4MqhPbDWVlFRUUsX76c5ORkWrZsCVCjKp1YpZ0cDgd/+tOf8Hq9ZGdn4/V6fTnsgMSB6YvGMbxeevbswcB+j5CXncm5s2cRQkeaUnXY66Rmtpew1l39SJCmbx3WFCboOh5TclvLZnTt0o5tmzezcd0H7Pj0MAMGD0aTJtILum6CEJgITKn5TYuBx+uxZ8fPnj3L66+/zl133cXIkSPt44esQovhmnt+PQSWeGrTpg2jRo3ivffeY8OGDb6fm14EBiZRIHSQBpquM+mZiZSePsnb8xfijIoCaeIBqgDTvzimSanC8asQ+b3ripggfHZDSIGQAlOCiYmBFzQdLxBduzZ9+/2MY19+yst/nUXLdt25q0MCDikQhhPT9GCYwm+BdF9uhvBiml4Mw5eZtnz5cnbu3ElqaiqtWrXyTSr541NL3IFljSL1YQnc7XYzbtw46tat6182O4VLN0F6MGQMpqmhSZ9XdGfC3Tz+2KPMzc7l2InT6MKXYlQlQAoNqYua2oGvGdU+XMyK0tABHWmaaEIgcNKzx304nTpr16xiXPIoGtavhzSlvxyRb8b8ogURCDR03YGmCQ4fPsw///lPevTowYgRIwCueBLnpXnckfgIpHXr1owbN47Nmzfz/vtFPqsNIIWvBf0Dn2GaPP10Ig0aNqBoy/tEudw4AR3/YoWUvm9qRqTzo6ih9W0D1q0DZ8ERIHTuaNmS2CgnEknTJs156OGHkaIWnbvchZCg6U4axsdTbmjowjdKmn6nXwqB5s+Qy8/P59ixY7z44ouUlpZy4cIFILROKAkGQgjuvfdeWrRowcyZM+nWtSPNm9+Gw+miWZMmRLtcAEgpuL1la377+//kP//4Z+rVqeOLw4VABE5sKh/9e6mxqapSWpNjlkU1ME0vXm8VJWVeoqNr4XJJNOGlstyD4RW4Y2KRAjRpUFlWjikhKi4OoWu+tVx8+dOa5mDXrt0kJ49lz549NGrUCLfbbZ8OWiObPADLqpeVlVFeXs7M/5vOhAkpeExBSWkZ0TGxRLldaBgITKqqvFwoKSEmpjYOK38AiY7h07bQUSq/MjVU4ODbtnDRkvsEL/3r2jqm9CVXCLyAQAgN0/S9XmCt3frPxbYTZXwTPpWVlTz33DRWrVqF0+mkrKyMtLQ0GjdubMfgCtiwYQOLFy+mZ8/uFOTnc3uLlui6AyE0JBIRsJFHCB0pBQbC/6mZ/udBKIF/LzXURYfLpx983cY33PmtMZrvIUyk9Po6kvR3Jil9D2HN4vrccgEUvV/E+vXrSUtLIyEhgRdeeIHbb7+dKVOm3ML7C22++OIL3nnnHfr06cPRY8fIzp3Hb3/zW4QwfXt1NIEvidXaZWYAGhoaQgorCA/uTYQBNVjgUH12xp//aHUeaeLPkvbNuAuJkCZI3e8WXvxNgYnEt6vp9NkzzJw9i4YNGzJmzBji4+PJz88nPT2dvn372jXPIz3R5fsQQmAYBvn5+XzxxRdkZ2fz3oqV5OcXMHzYcDp3ugfD8CLsrumfxZSAlLbkrb2iUijbfTVq9mxP4Py3PeNrfa9d/B4dgQMhdN9OJg38TwIC0wTTv+69etVq3t/8Ps8++yxt27alTp06TJs2jcOHD5OdnU1ZWZn996zoyFpCitSHdf6alZq6a9cu5s2bx+DBg+nVqxcp48fhcjiYMeP/KC0rRdP1aktsQmq+thc6COugRt+/1ULZ1VGtY8fh4uI/ESA0O91ZoCHQ8bnrl/+KlD6RHjlyhDlvvknnzp0ZOHCgPVveq1cvnnzySRYsWMD+/fsRQtgTbjXBilupqkIIKioqmD17Nrqu89xzzxETE8M999xDyoQUlixZwoYNm/zbb/3ZfqbPk/K1vQhod58L7/tcIr8NfyxK4DcAIQQej4fCwkIOHDjApEmTaNq0qV3oITY2ljFjxgCQnZ1NcXGxbd1qAoGWfNu2baxcuZIRI0bQsWNH26qPGDGC5s2bk52dRUlJiZ39VhMGwJtJzehhN4HAxQdN0zh69Ch5eXk8+OCD9OvXz36N9bqf/exnJCYmsnDhQrZv315jxA0Xq9WUlJTw8ssvEx8fz5gxY+zNJoZh0LJlS6ZNm0ZRURELFiyw3Xol8J9GzellNxCr9K81WVZRUUFmZibnz59nwoQJ1KlTx67iYh0I4Ha7GT16NLVr1yYjI4OysrIatSbucDhYunQpW7ZsYeLEiSQkJNg/tyz8kCFD6NKlC9nZ2Rw9ehTdH4srkf94lMB/BNZebqu22J49e8jNzWXYsGG29b40RdMwDDp06MC4ceNYsWIFixcvtjtwpCOE4OjRo2RkZNClSxc7bTfwedM0adCgAZMmTeLQoUO89dZbeL1eIHL3zN8KlMB/BIEliUpKSpg9eza1atUiOTn5qqJ1OBz28cDp6emcO3fuirnpkYaUkpycHD777DP+4z/+g0aNGl32vPW1f//+PPHEE+Tk5PDFF1/UqFDmZqBa70dgWRyn08maNWt47733SE1N5a677rqstnmg2A3DoGnTpqSmpvLJJ5+QnZ19xddFCtY97d27lwULFtC/f39+9rOffe+9er1eYmJiSEpKorS0lNzcXCorK6sNqIrrQwn8R2JVapk3bx7Nmzdn1KhR9nG/ga65tTXUegA89dRT3HfffWRnZ/PFF18AF0srR0on9nh8e+LLy8vJycmhrKyM1NRUYmNjL7tH6wRSq7xTr169GDZsGLm5uWzfvt0u3uj1eiPqcIhbgRL4j0TXdfLz8ykqKmLq1KnEx8df85lbtWvXZtq0aXz55ZcUFhbasSZEhpUKnGDcvn07hYWFjBo1il69el31/qyB0el0kpKSQt26dXnjjTeoqqqy95Qrrg/VYj8CTdM4dOgQc+bM4b777mPo0KHXNdMrhLCTX3Jzc9m2bRuapkXMspDlxZw7d47MzExq1arFiBEjcLlc17TZxuv10r59e8aOHcvatWtZuXIlTqcTiIwB8FaiBH4NWGu11rJWVVUVS5Ys4dixY6SlpdnLYtciTisXu27dukyePJmysjLefvttysrKfEUFw7QDB6aWWkuIGzZsYMmSJYwdO5bOnTtfsxW2BogJEybQvn17/vnPf9oHJkTCAHgrUQK/RqyOC/DJJ5+QkZHB0KFDefjhh4Hq+eQ/9D7W106dOvHoo4+yYMECdu7cGbYW3IqRAwdC0zR5/fXXueOOOxg5cqR9Xz+UnWYNlFJKGjVqRFpaGp988gmFhYW2lxOug2AwUAK/RizrUVJSwltvvUVZWRmjR48mLi7Ofv56MAyDuLg4UlNTqVevHrNmzaKqqupmXPpNx2oba4DSdZ2srCz27t3L1KlTadGihf26a3kvC6/Xy6OPPkq/fv3IzMxk//796oTS60QJ/BoIPLR+586d5OXlkZiYyH333WdbrmvFslBW4f/u3bszatQoli9fzvbt28O681oezJdffsn06dPp1asXycnJ1/Ue9g4y/6BRr149XnzxRY4ePcqiRYuU9b5OlMCvEdM08Xg8zJgxg2bNmpGamorD4bjuDme58E6n0465ExMTadeuHX/4wx84ffq07epe66x8KGC51V6vl8zMTE6ePMnUqVOrbYu91ve5tKR0QkICQ4cOJS8vj61bt9qvDbc2CgZK4NeI2+1m9erVbN68mbFjx9KuXTu8Xu91T/xYHTdwn3Tbtm2ZOHEiO3bsYNGiRZftnw4XdF1n27ZtFBYWkpiYSK9evew2uh4C2wigTp06pKamYhgGubm5lJSUXDbxqbgySuDXgK7rnDhxgpdffpmEhARGjRqFYRh2bfOf0sEsqzd8+HA6duxIbm4uhw4dsjdhhIvLrmkaxcXF5OfnI6Vk4sSJREdHX7cFvxKGYdC5c2dGjhzJihUr2LZtG6Zp2kcyh0sbBQMl8Gvk7bffZv/+/Tz//PPEx8fbcfSNmPmWUtKgQQNeeukl9u/fz7x588IysWP9+vUsXLiQsWPH0qZNGzvh5UbgcDgYO3YsTZo0YdasWZSUlAAoC/4DhFcPukUELvsA7Nu3j6ysLB566CF7WSwwBfWnYFlqgN69e9O/f38KCgrYtWtXSFsma07CaqezZ8+SkZFB8+bNSUpKIi4u7nsPPrherJAlISGB5ORk1qxZw5o1a+z3DeV2CjZK4FcgcC3WyqX+7rvv+PWvf01cXJz9/I1yoS1X0+12k5qayoULF8jLy6O4uPgG3M3NxQpR/vWvf7F161bGjh3LHXfcAXDDBBiYQDNkyBA6d+7Mq6++ysmTJ8POy7nVqNb5HiwXedeuXbzzzjsMGzaMhISEm16A4P777ycxMZHFixeza9eum/Z3biTHjh3jb3/7m31E040WndXehmFw22238cILL3Do0CEKCgqU9f4BlMCvgNVpSktLycnJwel02ud63+xlmdjYWJ5++ml0Xa9WhTXUsNpB0zTeeustDhw4wIQJE7jttttu+Ox/4AGG1p7xBx98kLlz57J///4b9nciESXwK2DFjdu3b2flypUkJSXRvXt3O+6+mSI3TZMuXbowZswYFi1axLp16+ytl6G25mtVs8nKyqJfv34MGDAAwzBu+Oy/tZXUWrVwuVy88MILnD59mvT0dCoqKgCuO+moJqAEfgVM06S0tJR//vOfNG7cmKeffrpa4sXN/ttut5sxY8bQsmVLZs6cSWlpabVsulBA0zQ8Hg/p6emUlJTwhz/8gbi4uJt2jYHxfFVVFV26dCElJYVFixbx8ccfA4bUjAoAABUZSURBVKj94ldACfwKaJrG8uXLWb9+PZMmTaJt27Z4vV67BtvNjPusEsytW7cmKSmJDz/8kKVLl4ZcmWVN0ygqKuLdd98lMTGRu+++284NuJkbQqSUuFwuNE1j5MiRxMXFkZeXx/nz5+3sQMVFVGv4Cdwtdvr0aWbNmkXnzp154okn7PXcG5G0cS1YA0hqaiqdOnVixowZHDt2rNprgrGrKvDvnTt3jtmzZxMXF0dKSkq1zLxbkXyi6zp33303qampvPfee2zcuPGya1QogdtYMa5pmqSnp3PgwAFefPFFGjZsaHfawBTTm4WmaXbpp4YNGzJp0iQOHDjAwoULgYsD0a2Oya2/a1Wf2bhxIxs3bmTcuHG0adPGbp/Adf2bQeDausPhYOjQoTRr1swuW60seHVUa/ixOsyePXvIzs5m8ODBDBo0qFo5pVt1HYFfBw8eTN++fcnKyrKTX26VlbwUKSUOh4MjR44wa9YsOnbsyPDhw+1NN7cq8STw3lu1akVaWhoffvgh7777bkjNU4QCSuBcdOvKy8vJzc2ltLSUn//858Dl9c1v9XXVrVuXX/ziF5w+fZr58+fj8XiCUmU0MCV36dKlbNu2jZ///Oe0bt066IcTWFt3X3/9dU6dOhW06whFaqzAAyurwMVJo0WLFpGSkkKnTp2A4AocfMLq2rUrQ4cOZeHChWzZssVOj73V8aZVi27u3Lk88MAD9OnTp1rWXzCQUlK7dm1SU1M5fvw4WVlZ9s+VNa+hAr90v7VVArmwsJDo6GiSkpKIiYnB6XTak2vBJDY2lvHjx+PxeJg7dy6lpaW3/Lqs2f3MzEy++eYbJk+eXO0Ag2C2kWEYPPbYYwwePJiMjAx27NhhX29Nn3SrkQIHLnNzV61aZVvvtm3bBvPSqmFN/HXq1IlRo0axbNmyoFR+0TSNzz77jIKCAh5//HEee+wx+7lgD4DWzr5p06bZYVZlZWWNORrqatRogVvpj+fPn+fNN9+kXbt2jBw50i7RGyoYhkFUVBRjx46lefPmvPrqq5w4ceKWzhhbiT+appGWllZtsg+Cuzxl/e0OHTqQkpLCu+++y7/+9a+bPqMfDtTYu7fym71eL4sXL2b37t1MmDCB22+/PaRiN+vUD8Mw6NixIxMnTmTDhg2sXr3afk3gSac3CiuGtd5z/fr1LFu2jJSUFLp3737ZrHmwrHjgsllUVBSTJ0+mfv36zJ07l9OnT9v3UlNj8hopcMv6SCk5evQof//733nggQfslNRQIXDt3ZpYe/LJJ7njjjtIT0/nxIkTN7XTWtl7xcXFZGRk0KhRI8aMGXPZUl2w2yywfW677TZGjx7N+vXrWbduHYBd4LImirxGCtyaZAOYP38+33zzDWlpacTGxob8hoXmzZszZcoU9u7dS0FBAXBxZ9eNtuCWcPLz89m6dSsvvPACzZs3D8lqM4F114cNG0aPHj3IyMjg22+/rZaFGGrXfbOpWXcbgNvt5pNPPiE3N5chQ4bQp08fe4052BbpakgpGTFiBD179iQzM5OvvvrKTjS50QOTw+Hg2LFj5OXl0bFjR5588kk7ky+U26hVq1aMHz+eHTt2sHr16mqrJTWNGiPwwKN1ACoqKsjMzMQ0TX7729/icrmAHz55I5hYLmatWrV49tlnOXnyJOnp6TdsB1VgG1m7xQoKCjhw4ABTpkyhXr161Y4mCkWsaxswYAB9+vThlVde4eDBg7YFD9XrvlnUCIFf2imFEGzcuJEVK1bYBQI1TbN3I4WqwANPEHnooYcYMmQIeXl5fPzxxzdkn/qlXsBnn31Geno6TzzxBAMHDrRr0IX67LRpmtSvX98eBPPy8myBh+pne7MI3U/pJmB9wKdPn2bOnDk0btzYPtc73IiOjmbcuHFIKcnPz6eysvInLe9ZwrYGiYqKCubNm0d5eTnjx48nJibmhlz3zcYaBA3D4P7777fPfgv3U2N+LDVC4JfGjO+//z6bN29m3LhxtGrVKmwOtAtMrzVNk+7duzNx4kTy8/OrLZv9FCwP5oMPPmDevHkkJSXRs2fPsGgfqB5muFwufvnLX6LrOjNmzKCqqqrGibxGCNzqnLquc+TIEV555RW6d+/O448/jqZpYVMFxBqorBTamJgYkpKSiI+PJz8/n7Nnz9orBD9mF5yVvltSUsLs2bOpV68eqampuN3usBG4NfNvhSzt27dnzJgxrFixgg0bNgC++/R4PGEzsP8UaoTAAbuu2ZIlS9i/fz+TJk2iefPm1U7ICAcskVsx8J133klycjLr1q1j1apV1Trs9cbk1nuuWrWKTZs2MWrUKNq0aXPLt8z+VALbyDAMEhMTadmyJW+88QbffPNN0DfI3EpqjMAdDgcHDx4kIyOD3r178/DDD1eLO8Pxw7Zmu62SSRkZGXz33Xc/uryTEIKzZ88yffp02rVrx7hx427YySTBQkpJq1ateP755/n4449Zvnz5DTlyKlyoEQK3Zp6tqh9Tp06lXr16YSvsQAzDoFWrViQlJbF7926WL19uu9o/dG+XPq9pGgsWLGDPnj1MnDiRxo0b21VSwxXLZe/Xrx9dunRh3rx5HD16NKzv6XqI2Lu0ygsFHj+0cOFCHn/8cR566CEAO1YLJxc9kECBPvbYY3Tt2pV//OMffPXVV9eUjBKYby6EYP/+/WRmZtKnTx+GDBlSbUksXAVhDe6B5a8KCwvxer0hvSR6owjPT+0aCFwzPn/+PK+88grR0dFMmjTJdjtDJZf6x2Jdu8fjoVmzZkyZMoVTp06Rm5t7zYNWYJrrvHnzOHHiBL/61a+oW7duWLeNhTUICiHo168fAwcOJDMz005+iXQiVuDWUomu66xfv55Vq1YxYcIE7rrrrrCbNLoagRNGffv2pU+fPmRnZ/PZZ59dUwe2RFxUVER+fj5Dhw6lc+fOEZPxZRiG3T6xsbGkpKRQXl7O3LlzqaysDPbl3XQiVuBWEcWzZ8+SnZ3NHXfcwbBhwyIym8nyVGJiYnjxxRcxTZO///3veDwe4OrlizRN49y5c2RlZeF2u5k0aRJRUVFhPzdhEbjRxDRNHn74YUaPHk1+fj7btm0Dbs5mnVAhYgVufVgLFiygqKiIqVOn0rx585AoUHCjsJaCAucRunbtylNPPcXSpUvZtGkTQLU03UCs+Hvbtm2sWrWKpKQkOnToYFu9SODS7bbgK9JYq1YtMjIyKC0trbYuHmlErMA1TePw4cMUFBRw//33M3jwYDRNi7gP8VIhOhwOJkyYQHR0NBkZGZw4ceKK8bgVvpw4cYIZM2bQokULEhMTcblcN/zwwFBB0zS8Xi/t27dn0qRJrF27lpUrV0Z0aaeIFbjH4yE/P5+9e/cyefJkGjRoUG3CJVIsVCBW+HHXXXfxq1/9ijVr1lBUVARceauklJK1a9dSVFTExIkTSUhIiPh0Tit0S05OtpNfLly4YB82EWlEjMAvLctz4MABcnJySEpKol+/ftVeG2lWPBCv14uu6/Tv35+2bduSkZFhr/sGlnYSQvDtt98yc+ZMOnfuzKBBg6oVRIjEzg4XCzTWq1ePZ599lt27d5ObmxuxiS8RJXCrA5eVlZGTk4NpmiQlJeF2uwGf+2o9IhEhhB1rtm3blrS0NLZu3cqyZcuoqqqyjzyycu9zcnI4fPgwzz33HPHx8bZ1i+RD/ALLYD3++OP06tWLOXPmcPDgwbDP2rsSEfMpBrrd27Zto6CggOHDh9OjR4+ItthXwrJEjz76KN26dSMrK4szZ85UO9Pr888/Jzs7m759+9K/f/+IjbsvJXA7aa1atezcgcLCwmBf2k0hogQupaSqqoo333yT+vXrM378+LDaCXUjkVLStGlTUlNTOXLkCOnp6YBvoqmyspJXX32V8vJy/v3f/73GtFFgLT7r37179yYlJYWsrCw+/PDDIF7dzSGoAg9MlQz8GlgB89JSS1d7LyEEy5YtY9OmTaSlpZGQkFCjCu0FZuZZ3szQoUMZOHAgs2bN4sCBA2iaxubNm1m8eDHJycl06dKlxng4l1apFULgdrsZNWoUhmGQnZ1NaWmpPRBcS5+7tLx0YH8NhUEzqD3fipmt/cvW6BrYaIElb6+GlJJTp07ZO6GSk5Mvez7SH1Z7Brar2+22jz2aM2cOZ86cITc3l9q1a5OUlARQbQAM9j3c7Mel92gYBgkJCYwcOZJly5bxwQcf2APetfQ76zXWV8uTDAVxAwR9tsnKwtI0K1mjeoezki58r/n+8UjTNAoLCzl8+DCvv/46devWtd+/pvB99/rwww+TmprK/PnzKSkpoaioiN/97nfcfffd9msicYLpWrCShJ555hk++OADZs+eTY8ePewSVVfrP1LKahO2lrBDqc8FVeCBBfRLSi5w+PARSktLAahVqxZt2rQhOjr6mhpt7969ZGZm0qJFC+Li4uw0xJqMzxJJNE2nW7duZGRkkDV3Lh06dCA2Npbt27fj8Xj9Lr0EIjM/4GpYllYIQUJCAgsWLGDNmjV2WvPVME2Tzz//nLNnzxIfH0+LFi2qJc2EQlsKGURfQhomXmnidAiKNqwiZfKvcUU5qR2l44qJpm+fAYyfkMptt9+GjoFD87vwODER4LfqhmHwl7/8hZdeesmu0FJT4sqr4dB0TPydTRNICZ6qqmqZbb7BE//3wbrS4BIoRK/Xy3333cfChQuJbxyPrulIAaYAIT1getA0weEjx1i4aCmLChdTXFzM7S1a8OjgQQwfPpwmTeJ97aoFX+DBddGFhq8NvBhVZ4mJq8/v//wHut15G5/s28Of/vwXTN3N//uP/0e0A8C3ecIUGqZ0gD9OLykpoVu3bsyYMSNiExauBVNIhO8bhASBQAqJFCAxEUJHCA2BRNoDoPQ/IIIWVX4UgZ6ix+PxNYtpYgqBqYGGF50KDn91lN//8b/57rvzPDPlGe68806+PPQlK1as4M527WjSNB7DMNFF8PebBz0Gt7qWQOBwOmhzZxvaJNzB7W3uYMHbizl27ChejwccDhAaSNPXiaW0xRwTE2PX7VYobgQerwcpDaTQQOggJBoC0Fm25D32fPo501+bQe+f9UJKuPfeHjzc5yF03YHXaxIq4U7QBR6IlFB8vpjK4mJ27NnJyRPf8vgDD+JwOTEFgPA9pEBIgWka9tKHNYtckzElmICG9D9ACg2haXilxPRUAfirtOgYpq8jWghqpudjYc2Ga5qGJjTABGGCJhD4vKMLZ8/zwZaP6dSpJ53u6WxXDhJC0KBBA3+4Y4bMQQvBFbhvXgfLTTx39izPT32WRjGCb05+y/297mfQwAEITWBIExMdTeKbaRcg/GdyBbsRQ4FAJ1tIEMI32Jmml6NHjvP2osUse6cQl1NnwMBBPDXyaZo0a4rucOIxDNxOJ1oNb8fAarX2z/CfhgMgTYovFHPiu9N0vvceomOi0TThHzAFhmGGXF8M7ix64PcSYqKjGJ+axt2tGnO++Bzz5uXxxz/8J//9yqs0a9IIaQ0GppXUERozlaGC1RJCmAgkhtfDwkXv8Mo/ZtCwcROeTkzE8FaycuUq5uUX8D//+7/0eaSfbc0dDhXiVEfDN4GhIYQBQmBWeSgrK/d7RgLfKgVYRkpK0zfPYXucwSVkXHQpwOmKok/fh+hxd1tA0qBeHL/63Z/Zu28/TZvGI/0mX4RAw4U2AoTOkSNf8Or01+jSpRv/+9e/UyfODQiSRo9m8jPP8uqr0+lx3/3ExdVG6AEOlcKHFBjS1zeFIUEziatdiyZNmvDdyROUV1TijHFj+U8Xl8isHXvBn7QMbqqq3ZsEptQRQmIaBvhj6Vq1aqHrGqbX67tQ/2iquuHlWC0ikb64EcnWrVtBSsaOG0d0VDSeyko85SU0atiQSWmpHDx0iH37PwNd1Nglsqshwd/n/D8wJXXr16dL13vYueNjDh78wv+EBmicO3+G8xfOYcrQGSqDPMRITMML0oF01EOnHKP8Ah7D5NChQ8yYlUnDBo3o1K4NTtPEt8CjI4Vv+UdRHSkMDCpBesHr4eihIzRu0Jjbmt0GDpAOp28lwqyiS9eOuGOi+OLoMbwCTK2mT7FdjhASTTPRheFbzhVOhDua4U8NpXnjOJ5/dgrZ2bl8/vkhcnLyGDN6Aps3FqFrTqQZfOsNQXbRJdLnbgsN3R2Lx1PB1CnP4HK5iI6OpkOHDvz+51NocVszNGki0ENlYAxZfBbc953X8OJyuNA1HQ0whY7udIBZidupozt0isvK/L+oJiuvRLXFG1NDSoP2HTrw3//zZ7Ky85k+fTrTp79Gw4YN6N+/H127dcc0CZnBMuipqkIIqqqq6Na1K1u2bLGXvKSUOJ1OO51V8cP4+qHfcuiSqKgozhcXU15RAYAhTd8HrmmcOHGC8tIymsTH+14fOl5lCHFJgwiJ4TURAjp26sTf/uYTs8fjrXYckmlap8EEv0GD6kfYa46ahtPpxOVyoeu6/X3gaxRXx2cxNHQ0v1hdtG3XjuPffc2+vZ/iwJe6qukO0DSWL11GTEwsXTt1QhoSYSUQKaoj/Obb//AJ2ffwzaBrOJ0OdN3XR31ffSKXMviGKagW3Mo8s46Qsda0A/OkL82bVlwZgW+0llxc6urWozvNW9zOa9NfpVadOnTr2YPK0rO8t+gtsrJySZ367zSNb3wxKUa56d+DbzlMCN/qhBVaCt2XdKXrjmpbUa3Z9FCYRQ/uZpMf+NOqs10fUvr/J0wkBqZp8NFHHzFzxpscPfINMXVqoZmVUFnGgc8P8vDAJ5jw82fp1rUTDtMbtme03UzkZf+S1Z65+pKtZfmDhxJ4JCH9bSpMTLz2zrozp85w9MhxTp07S5RLcHt8A86fu8Bvfv8/fP7V1/zbvz3HM5NScbudwb6DkCJQzlf6qZW++v0EPw5XAo8kpN+KB1hwIQS65sSXoe53Ns1KBHD8u7MsfGcJDl1j8sQ0NF21dyCX22sfAon05/sL+1kR8CqrHWu4wBU3k+pd0vrJpd8prs73iUNc9dmLrwg2SuAKRQQT/Gk+hUJx01ACVygiGCVwhSKCUQJXKCIYJXCFIoJRAlcoIhglcIUiglECVygiGCVwhSKCUQJXKCIYJXCFIoJRAlcoIhglcIUiglECVygiGCVwhSKCUQJXKCIYJXCFIoJRAlcoIhglcIUiglECVygiGCVwhSKCUQJXKCIYJXCFIoL5/ylvwv6x/Kh9AAAAAElFTkSuQmCC)
Use △ ABC, where M, N, Q are midpoints of the sides.
MQ = 3y − 5, AC = 4y + 2
![](data:image/png;base64,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)
Maths-General
Maths-
M and N are midpoints of the sides AB and AC respectively.
Which of the given statements is NOT correct?
![](data:image/png;base64,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)
M and N are midpoints of the sides AB and AC respectively.
Which of the given statements is NOT correct?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOAAAADLCAYAAAB3Rp8UAAAgAElEQVR4nO3deXhV5aHv8e/7rr2TECaDVAaxyHBAKwqVMsgsiq0iKIoMBkgMJCCt1vvQeryPz2mf9t5zTm/vOb3SUuZgwowDk5QZQWYOCFoBsSAIRBkDCGTae633vX/srM0OCAchydrD+3mebUIm1957/dY7r1dorTWGYXhCen0AhpHITAANw0MmgIbhIRNAw/CQCaBheMgE0DA8ZAJoGB4yATQMD5kAGoaHTAANw0MmgIbhIRNAw/CQCaBheMgE0DA8ZAJoGB4yATQMD5kAGoaHTAANw0MmgIbhIRNAw/CQCaBheMgE0DA8ZAJoGB4yATQMD5kAGoaHTAANw0MmgIbhIRNAw/CQCaBheMgE0DA8ZAJoGB4yATQMD5kAGoaHTAANw0MmgIbhIRNAw/CQCWDcUoAO/0sDWuvQZ9oBHfq+vs5vG9XD5/UBGJVIAwJC4VOhf2gLDdhao7QiSSpQNkJINBIlLATSXIk9Yl73uBYq3wSAXYZTepnCwnMEHIEjfCgshFZIlKdHmchMAOOJ+K6vKRAKvwgya/pkMjKz2HvoKEpYKCEQbrXU8IQJYBzRWpc/BFpLlNIoFQRszheeZMO6tXzzzSnWbdhEQIHSApM/b5kAxpWIThcd+pejgoDD1i3bSK5Rh+zsHNavWcPZM+fwCRBI0N9VdBrVwQQwbmnQGssSBJ1SVm/axkM/6UKvHt25fPYUBz/7FAtQSLQwp4FXzCsfRyJrk1qD1gopBEe+PETB14X8tP+z3P+jVjz4o39i84b12LbCxtRAvWQCGEe0kCgh0EIjhEYoGzRs37iNC+cusWvXThYtfg9fchLrN+7k+MlClBRmNNBDZhwwDmlAopE+H5cvnGfTxi04doBNH61HqWJsW3Py9Am2b9vBcy88jfjO7lOjOpgAxpPwQLxAIwDJl4eP8M3pM/zbv/9vunTpgq0voYIwbtybrF23nH4DfkaSz5wGXjFV0DgihUaWR08jQFh8svdz0u6sT8tWzdEEsfDj9/vp2esRvjryD44d/cqUfx4SOjRB0IgDOqI15zgOynE4duw4ZWWltL6vBT7Lh1ASjc35b8/wxT+OcG/LB2hwZz1zJfaICWAc0ajy8g+UUti2g5A+pARBGZbwgeNDCBtHF6OtZBw7Gb9PIE0x6Alz4YsnEZdSKQXSstDaQTkKsACJIDRLRotQu88MAXrLlIBxSl/1DxH6D6EVEoDQ5d8KFX2mAPSGCaBheMhUQAzDQyaACUJrjVIq/NGIDiaACUIphRDChC/KmAAmCCklp0+fNgGMMiaAccytcgKcOHGC3/72t+zduxcpZbgqagLpLRPAOOWGyw3hokWLmDp1KlOmTCEQCCCEiFhBbzrCvWICGKfcgAkhOHjwIDNnzqRNmzasW7eOLVu2VPg5wzsmgHEuEAgwbdq08Mc2bdowYcIEzp49G/4ZE0LvmADGKa01Pp+PAwcOsGzZMtLT0+nUqRNjx45l165drF27FikljuOYKqiHTADjlBCCQCDAW2+9RePGjXnhhRcA6NKlCz169GDatGmcPn0an89nSkAPmQDGKSEEmzZtYsWKFeTk5NC0aVNs2yY1NZVf/vKXfPPNN8ybNy/cVjS8YQIYRyKHFi5cuMD48ePp1KkTP/3pT9FaI6VEKcXDDz/MgAEDmDt3Ll988UV4gN70iFY/E8A4opTCcRyEECxdupRPP/2UN998kzp16gChwXjLspBSkpWVxeXLl3n77bexbRutdfijUX1MAOOI1hrLsjh+/DgzZsygT58+tGvXjmAwWCFYWmuaN29OVlYW7733Hvv378eyLFMCesAEMI64Vcw5c+Zw9uxZxo4dS1JSElLKCh0t7vjgkCFDuPfeexk/fjzFxcUIIUyHTDUzAYxxke0+KSVHjhxhwYIFDBw4kHbt2iGEwO/3VwiWEALbtmnSpAljxoxh9erVbN68GZ/PZ0rAamYCGMPcsEgpw/M7J06cSHJyMsOGDcOyrOv+rjsG+MQTT9CuXTsmTpxIYWGhKQGrmQlgHNm9ezeLFy8mMzOTli1bXvfn3OAqpahTpw6vv/46+/fvZ/ny5UhpTonqZF7tOHH58mX+8pe/cPfddzNgwIAbrnJw23puCdm+fXt69epFfn4+x48fByou4DWqjglgDItcYLt69WrWrVvHG2+8QcOGDW8YHCFEuNoKkJqaypgxY/j666+ZM2dOeDjDTFOreiaAMSxyrV9+fj7t27end+/e33uNn+M4tG3blkGDBpGXl8exY8fC4TRtwqplAhjD3HAsWrSIAwcO8Nprr5GamhoeZrhZ7s8PGzaM2rVr86c//YlAIGBKv2pgAhhj3LaZO2ulsLCQmTNn0rt3b7p06QJQoXp5M3/P7UFt1aoVGRkZLFmyhN27d4cH542qYwIYYyJnqyilmDRpEkVFRYwePZqkpCTg1quNjuOQnp5OkyZNmDBhAhcvXjS9olXMvLoxSCkVXus3Z84c0tPTadeuXaWUVmlpabz55pts376dDRs2VMLRGjdiAhhj3PZaSUkJU6dOpVatWgwdOvSWJ1K7QxLudDWtNV27dqVz587k5uZy9uzZ0E5L5gZOVcIEMMa4K9137drFBx98wGuvvUbTpk1vq/SLDCFA3bp1GTVqFPv27WPx4sVYlmVWSlQRE8AYY1kWFy5c4M9//jP33XcfTz31VPimu5U1ZBAIBOjUqRN9+/Zl0qRJnDp16obT2oxbZwIYI9zSRwjBihUr2LFjB2PHjqV+/frhqmFllFBuiFNTU3n55ZcpKytjwoQJpvpZRUwAY4DbBtNac+7cOWbMmEHXrl3p1asXECoV3YW2lcHtTX3ggQcYPnw48+fPD68ZNG3BymUCGCPc4YfZs2dz9OhRXnnlFWrWrBnulKnsGSvu3xs+fDi1a9dmxowZlJWVVVh5Ydw+E8Ao5wZPCMHhw4fJy8tjwIABdOzY8XvPeLkVjRo1Yty4caxZs4bt27dX6f8rEZkAxgB30vWsWbMIBAJkZGSEq4PVURL17t2bli1bMmnSJL799ltz64pKZAIYAyzLYt++fSxYsIDs7Gx+9KMfVVsAtNY0atSIkSNHsmXLFlatWlXhLmrG7TEBjAGlpaX85S9/oUGDBjz//PPVWgK5/5/evXvTrVs3pk2bxoULFwCzUqIymABGOSEE69evZ82aNYwZM4YmTZpUWKdX1SFwb11Rs2ZNXn/9dY4cOUJeXp4ZF6wkJoBRyF0Qa9s2586dY/r06Tz44IM8+eSTwJVhh+oIQeQ0tR//+Mf079+f/Px8Dh8+DBBeuGuGJm6NCWAU8/l8LF68mD179jBu3Djq1q1bYdihuqqAkf+v7OxsgsEgeXl5BIPB8NdNdfTWmABGKSklJ06cYPbs2eG1fu5dr73UunVrsrOzef/998O77Zr9JW6dCWAUckM2d+5cCgoKyMnJISUlxfO1ee6c02eeeYb69eszfvx4ioqKcBzH0+OKZSaAUcgddM/NzWXEiBF07NgRwPMAQqjNd++99zJmzBjWrVvH5s2b8fv9Xh9WzPL+HTWuYds2EydOJDU1lUGDBnl9OGFuVTMYDPLkk0/Stm3b8LCEqYLeGhPAKBF5Au/cuZOFCxeSlZVFq1atPDyq7yaEoG7duvzyl7/k448/Dq8ZhMpZkZFITACjhDvsUFxcTF5eHvXq1WPw4MHX7GzkJSEEPp8vvPKiW7du9OjRg7fffpvTp08DmNUS35MJYBRw70wmpWT58uWsWbOG3/zmN9SrV8/rQ7tG5JBEjRo1+MUvfsGpU6eYMWOG2eTzFpgARgF3sPvixYvk5eXRvn17evToEfXzLR3HoUOHDqSnpzN37lwOHjxolip9TyaAHnFLisgq25IlSzhw4ADZ2dmkpaWFq3zRyJ0QoLVm0KBB+P1+pk2bhm3bZpra92AC6KHI8J0/f54JEybQr18/Hn/8ceDKDXa9Hny/Edu2adWqFVlZWSxcuJDdu3dH9fFGGxNAj7gliDu2N3nyZIqKisjMzIyK8b6bETkt7oUXXqBp06ZMnz6dy5cve31oMSM23uk45e5qu3fvXubMmcOwYcNo27ZtTPQiRpZyjuNw11138corr/Dhhx/y4YcfAmaLs5thAughIQSlpaXMmjWL5ORk0tPTY+pkvXpVxmOPPcbDDz/MxIkTOX/+vNni7CaYAHrE3SBzx44dLFmyhLFjx3LPPfdg23ZMtaHcY1VKUbduXbKzs9m/fz+LFi0KdyCZAF6fCeB/69qTR1f4mr7BT16fUoqioiKmTp1K8+bN6devX0yvLNBaY9s2jz32GP3792f69Ol8/fXXWJYVUxeU6mYCGEEDGoVGoxRoR6GCxTj2eYLBEhwbgkpRGiwlaCuUrUCVolUxpXaQUuUQUDZaabQOcnVTzu31VEphWRYrV65k69at5OTkcNddd6G1rtT7e1Ynt8fW5/Px85//nHPnzpGbm3tNia6AMkfjBMtwAiXYdhBbaYKOIhgMoANlBOwApY6NchSOUijHwca+6sIXH2Lvna5yoRhqDWiNtGw+WPIugwen8857H2CjEZYEJQBFWcll/t9//gdZI8ew85N95eHRwLVLdNyxP601Fy9eZMqUKXTv3p2f/exnANW6yLayRfbo3n///WRmZjJ//nz27dt3zXNSSmNJ+NvSRWRmZLBp63aEJRFScvbkCf74xz+wZ99nSEuWh07hoOIwfiaA1xEKodACHMVne/fz0ZYdTJiYy+nT55FSIISD9MFnn37GRx9uZfWajRw8eAxf5Et6VZYiN0GZO3cuhw4dYtSoUdSoUSMmq503MnDgQGrXrs2cOXMoKysLf10AfqnAknyx7zPWrl7Dn976M6cKv8WyfBQXFbPxo484dfJkxG9EfowvJoARtFbhKqgQoesuQmPb0PXRRykJlrBl02Z8+JA4BEsusWHdR3Tr0pNmTVuCcl9OAejvPGeklBw7dowZM2YwcOBAunbtim3b1fk0q5zWmmbNmjF69GgWLFjAxx9/HP46WmMJBdpGCk3//v04deIUK1asRgC+pCQs6UdIdzaNAC3LG9jxF0ITwGuo8odGWgKEBg13Nbibvv37sGbVKooulSH9UPD1MT79ZD8dOnQkOTkZHa52fndpppQiGAwyc+ZMSkpKeOmll+K2k0JKydNPP02rVq0YP348xcXF2LaNclfPC41WDv/UvBmDX3ie+XPn8vU3J5HCh0Cgw+1nUf6Iz1M1Pp/VLdFcCU5EgARoBBaSJx7vyleHv+SzT/YCFtt37aRGnTTuf7AVtipGOZElmajwZ9wOlk8//ZQ5c+aQk5PDfffdh23bUT/d7Fa4g/M///nP2bZtG8uWLcPv94eep5aARGuBQDF40HNIHeS9d99BSguNhZSR80nj67WJZAJYwdUhDFWZhNYI5dCy2T38sEljtm3dxqVL51i1dj1devTkzjvroJwShKXCv3l1AIUQBAKB8Fq/Z599NjzkEI9LeBzHIRgM0rdvX7p06UJ+fj6FhYUIKdEiFECEwHE0jRo2ZNDzz7Jq2RK+PHQodEG6JnTXfiUemACW0+hQtQgfSvtRSqO1AiFBWChhkZbWkD69u7Nzx4es+NtKPv/iazr36IElLSzl4CvvqdNCgBYIbOxgMDy1bOvWrfztb38jMzOTe+65J1wqxmM11O/3Y1kWycnJvPHGG+zZs4d58+ahNASlAGws4WAjKdGCQYOeo1H9O5gzNz90UrrtaaEQwsGPRsTXNQowAfwOEiEkINBKgwKNRKFRStKzV3fOnz/Nv/zL7+nS/VF+eO89lAWc0NXZUeHSTwBK2SBCbZiioiImTZpEmzZtKkw5u7oUjIeH+7zc5/bQQw/x4osvkpeXx6HDX4ZeZmWHpqohCWqoWbsWL6Y/x9oPV/LVV0dJ8fvLL2YKIRQy+qfH3hITwHKR5Y8GhJTl4fERCNo4wQASTZN77uWhh37MhYvf8uLQwQgRGqlydHnvacRfFEKWDzsIFi5cyCeffMK4ceOoWbNmhZvrxvtDSkl2djapqanMnTMHx7ZB+AjYGuUoLKGxHcUjPXrS56dPcKygIFxrKO9PJl7bgULHW+PjlmmUdtBCosOlXxCpbf5r525KlJ9uj3QkSWr2fbaHQ0eO0+ep/kgpkMFSlq9cTesHHqR1yxZoNFI7oDVIH4WFhQwaNIhdu3YxcOBAkpOTY2LFQ2Vxd1PauHEjl4ous3zVSh66ryUfb9+B9tfkgYd/gp8y/DLIV18dZ/Pm3XTv1Zsm9zQEglhKgvaFios4y6EJYAUKhQgFsHw2i6U0QvpwEKExLO2UtwsltgYEWNpBCKvC4IPQGo0CJLm5ufz+97+vsLFKIr3skW3dLw8f5rkXBvDX8X9GORrpS8IRYGkbSRCED/CjdWhaIMJGKInAF5/1NW1cobRWWuug1jqglQ5opW2ltKOUdpSjleNobSutba2V42hHOdrWTuj7jqOVckJ/JMIXX3yhH3zwQf273/3Oi2cUFQKBQPjzmTPzddN779Gr1q7VjtY6aKvy1zGobR3Qjg5q5bivsa2VLtVK2dpxvDv+qhSP15Tb5JZ/uvwzUV6yhQbnw+PCGkR5eXn177uCtk1eXh6O4zB48ODQd6Ogk6S6H1JKbDvU6fL88wNo88D9TJ2Wy7mLl7EsgdQKtMQhohYhNCLUAxbXTAAjiVD/pSwfeLcAKUAKgRRWqGNGitAQliURwkIiQ98vH0xXSof3Svh41y7ef/99Ro0aRYsWLdBaV3sHSDQ83JUSUkpSU2vzP14bx87t2/jb0qXl17JQm1sqjYVEhF50kBZC+BBCEoMLRG5KnD6t2yMAq/xxpd0vuLYH4OqvhQIIUFJSQn5+Pg0aNCA9Pb2qDzmquSF0xzq7duvBT5/oQ/6M6Zw9exal3clmV085k4TehTjreYlgAliJ3BJOSsmqVatYvnw5L7/8MnfeeWf4+wakpKSQkZHBmTNnmDNnDnDl/jGJxgSwErnhKy4uZsqUKXTo0IG+ffuGZ7q4JUCiCwaDdO7cmQEDBjB16lSOHj0al/Nhb4YJYCUTQrB48WIOHDhATk4OderUAYjL6Wa3IrKWkJ6ejmVZTJ8+Pbz3YKIxAaxkBQUFjB8/nieffJI+ffp4fThRxw2fbdu0bNmSnJwcFi5cyMcffxyTt+K4XYn3jKuA27bTWjN//nxOnz5NdnZ2Ql7Rb0Zkb/DgwYNp2LAh+fn5FBcXe31o1c4E8DZprcMr2vft28fs2bPJzs6mXbt2ptPlOizLwufzIaXkBz/4AWPGjGHp0qWsWbMGIHw/0UTolDEBvE3uQHNZWRmzZ8+mRo0aDB06FCGurHIwrk9rzVNPPUWnTp2YMmUKFy9eDL92icAE8DYJEbrB7s6dO3n33XcZNmwYP/zhD0O3X0jQjoXvw3EcatWqxahRozh06BBLlizx+pCqlQngLYi8v6fWoZkvkyZNolmzZgwcOBCfzxfubDBuTAiB4zg8/vjjPPbYY0ycOJGCgoKE6TU2Z8gtctt+Uko++OADNm7cSE5ODg0aNACI2RvsVje3Q8bv9zNy5EjOnDnDggULEmZPCXOG3AJ3fVtSUhJnzpxh4sSJ9OzZk2eeecbrQ4s57kXKtm3atm1LZmZm+J6piXABi/9nWAXcjhfHccK72ubk5JCUlJQQPXdVQWuN3+9nyJAh+P1+3n777YR4LU0Ab4Hb8XL06FFyc3N54YUX6Ny5c7g6Zdw8KWV4WEIpRYsWLcjKymLWrFls2bIFINyhFY9MAG+BUgrbtpk7dy7FxcWMGDGCpKQkrw8rZkUuXbJtm0GDBtG6dWv++te/UlRUhFIqvMQr3pgA3gJ3V9v8/HyGDh3K/fffb3aCrQTu65eWlsarr77Krl27WLZsWXgD0HhkAniT3OEGx3EQQpCbm0vdunUZMmQISUlJ4XahqYLeOnd7M601ffv2pUOHDuTm5lJYWBje7DPemADeBHetmruv39q1a1m+fDmjR4+madOmgFntUFnc8dOkpCRGjx7N0aNHWbp0adzWLkwAb4L75luWxblz55g4cSKtWrVi2LBhCTNe5YVHHnmEAQMGMHnyZAoKCrw+nCphAngTpJThKubatWvZvn07v/jFL0hJSQEwJV8VSU5OZtCgQZSWljJ//nyvD6dKmADeBF1+X8tTp04xefJk+vbtS69evcx0syqmlKJdu3aMGDGCadOmsXfvXiC0oj5eah3m7PkeFi9ezDfffENGRgY1a9aM27GpaOGGbMSIEdSoUYOpU6dSVlYWVxe9+HkmVUgIwaFDh5g8eTLPPPMMHTt2rDAZ26g6tm3TsGFDXnvtNVauXMm6deviqsPLBPAG3JABzJ07l5KSErKyssKD7uZGS1XPnSEzePBgWrRoQV5eHt9++y1w5SbHsVwTMQG8Djd8Ukq2bt3KggULyMnJCd9g151CFU/VoWjjvr5SSmrWrEl2djZ79uxhxYoVQMVlYbHKnD3X4S6mLS0tZfr06aSlpZGenp5Qq7WjTZ8+fXj00UeZMmUKly5dCr8XsXwRjN0jrwaWZbFx40bWrl3LqFGjuOuuu8wqd49oralduzYZGRkUFBQwa9ascBMgli+IZnuy63Ach6KiIoYMGUK9evWYPn06KSkpOI4T13MTo1Xk/XXefPNN3n//fVasWEGLFi3CTYVYFJtHXQ3cle6HDh1i2LBhpKSkxPQbHQ/c2kdWVhZCCGbOnElZWZnXh3VbzNl0HQUFBUyYMIFHH32UHj16hNf6mTudeUspRfPmzXn11VeZN29ezN/QN3aPvIq44VqyZAknT55k1KhR1KhRI9zuM0MP3nAXQbsf3Rv65ubmUlJSUmG1SiwxASznvoFaa/bu3Utubi7Dhw/n4YcfDg+4m/B5K3LqX/369Rk5ciTr169n/fr1FWolsVRDMQEs5wZMKcXs2bOxLIuXXnoJy7LMrSaikOM49O/fn44dO4Zv6AuxNzHeBLCc+8bt2rWLefPmMWTIEJo2bWo6XqKU1pq0tDQyMjL45JNPWLp0KZZlxdwwUUIPQ7gdKm7Vsri4mOzsbM6ePcu7775LnTp1wtWZWHpTE4G7H4fWmrFjx7J3717ee+897r77bo+P7PtJ+Et7ZLBWr17Ntm3byMzMDO/rZ9p90cmdpub3+xk7diyFhYUsXLgw5hZIJ3wA3SrLmTNnmDp1Kh06dKBfv34xPb8wUbgTsR988EFGjBhBbm4un3/+eUxdMBM6gJFjeitXruQf//gH2dnZ1KpVK6auoonKvQmWz+fjxRdfRErJzJkzw1ubudXUaJbwARRCcOTIEcaPH0///v3p3LkzjuOYjpcoF3kvUa01TZs2JSsriyVLlrB58+bwz0R7TSahzzJ3Jv2CBQu4dOkSGRkZ1KpVK+rfNKMit7YydOhQmjZtypQpUyguLg7fyyeaJVwAI7eT9vl87N+/n/z8fF588UXatGmDbdsx1YYwCO/TkZaWxsiRI9mxYwdr166Nifcx4QIIoS5sd3ux3Nxcateuzcsvvxzeo8Dd38+IHW57sF+/fnTo0IEpU6ZQWFgY9StXEiqA7nQzd0rTli1bWLZsGTk5OdSvX9/rwzNugzsIn5qaSnZ2NgcPHgyvnI9mCRVAt9EupeTbb79l0qRJtGzZkoEDB3p9aMZtiJxQAdC9e3eee+453nrrLY4dO+bx0d1YQgXQJYRg/fr17Nixg+zsbO64446ob6wb1+deVN0e0aSkJNLT07lw4QKzZ8+ucPOmaHufEyqA7ptQWFjI+PHj6dmzJ7169TJr/OJE5BZnDz30EMOHD2fevHns3r0biM5VEgkVQAC/38/ChQs5fPgwmZmZ3HHHHWbYIc64JeHo0aNJTU1l3rx5UTsonxABjGwjfPnll0yYMIFnn32Wbt26hXtEzcB7/HAD2KBBA0aOHMmSJUvYsGFDhXm90VIaJsRZ566Utm2bmTNnEggE+NWvfoXP58Pv9+Pz+UwA44h7z1YhBEOGDKF169ZMmjSJkpISILpu6JsQZ5278ePOnTtZtGgRGRkZNG7cOCreAKNq1alTh5deeok9e/awYcMG4MoUxGgY6437ALohCwaD5OXlUa9ePYYPH27Cl0CeeuopevXqxR/+8AcKCwuRUkbN+x/VAXSrCpE71EZ+7lYtb/Riur+/adMm1q1bx4gRI2jcuHHUXAGNqqW1pkaNGowZM4ajR48yb948gP/2vIk8xyLPvcruMY/qFfHuWr3IJ+2Gxl2x4FYnrjflSCnFxYsXyczMxOfzMXnyZOrVq4dt2/j9/mp7LoZ33BC98cYbbNu2jby8PFq1aoXjONfde95d2OuOMbrnX+Q5VxmiugR0O0au3gzFDZz7+Y1eDCklq1at4u9//zujR4+mfv364T3II5e0mEf8Pnw+H0lJSbzyyisEg0HeeecdbNu+4TzRUL+BFe7McTeJqezyKqpLQFBoBALNRx+uY2puHsLyk+wT9OzZk6f7PUPtO+5AAD55JYQacP91/Phxnn/+eXbv3k2fPn3w+XxmvV+CcYOolGL79u2kpKTw7jvv8EiXLkDofAEQKNAKhMVXX33F/PnvsHffXu5/4AGeH/AcLVq0wLIkgsq7R1AUn4UKrRWOBnD44pNtFHz9DX36P8+jPbuzYPZMfve//pXLARuFQGsbrRycq64nx48fp1mzZjz99NOkpKQgxJUbvJpH4jwgVKp1796d9u3bc/ToUZxgEK3A1uBojQqWoINFfLhmGcNHDOOzzw/QrcejnDh5mn//P3/kwMFDKCGwK7HM+u4KcNTRKMehSZO7ebrfU9yZbBEsLWHWux9w+XIRNe+8A7QGodFCcKX8gy5dutCl/EpnGJGCgVIEEi2s8maO4OzZQv79//4nj3TryW9+81tqpSRT5igOfPEFd6SFZk3JxAsgSBma43fu3EXwlXHwH4do2bIlKbyrmQ8AAAMWSURBVCk10BoQGlCEwnclhG5PVuhvyEqrOhixKbJzxbIkCAcQCKGRVhJ7/r6fYycK+dfBQ0hNSSbgOKA1D9zXGqU02nEQlbjGMGYC6Lf8fLxrN//z1/+MvniCUye+5uVxb1AzNQmFCgVQw5UafUhkldMwIjteBMFwf0Go/edw9FgBaXc1ot4PGiAAKa609ywpEKJyIxMzAXSUQ7PmzRmWkU79ZMXG9av461/H0+L++3n4oTZcqXZKIqugkW0Aw4g8FzQWGgVopFagbKRykG5lCgcJaO3eHV0ACiEqr+skZgKolKJhwx/QtUc3fpBs0b59K7Z/+nc2btnEj9u2AS1Bi9DHKO5aMqKHRqKQCARCAVLww4YNOfvNSc6dOUPLJg1QOhiqqiLQSoEQiTMOeKUyKXCUBQr85bMXzp2/RPHlYurVroUvot0nMKWdcbMEAhnqPggVbjzUti2N7kpjZl4up86exLIsLl6+xI6dOzhx6iQASiVAJ4xGYgvAsUFaKFLY/+mn5E76M6l1a7H7v3ZyZ1oDnujZC6EUCAkCZPnIoWH8d0LlWqj/QAgL7SjqN27Mr//5Vf7tD/9BzuiX+Un7n1BQUEBR0WV+/evXadTwboRIgKloGrBxQDv4lcXePZ+wau0aypSDsgT33tOU7l270ahRo2vuYmbafMbNcU/9UDvQcezQ/FCh+PzAIbZt20Vh4WkaNWpM506dadGiBUIKpJBYlTSRI7oDqO3QLBcNIMGdmsaVbpZAIGACaNym0ERrxw6ihUYI8FkpgKhwrrlDGNKykJV0jkVtAAFsbIQGCwFaoxEgQn0toQ6X7w6bCaDx/ejyR2j2lRACpQQQCpomNMSluTIhu7JEdQC1DlUNoGKpF/rcDKoblc0df9Ch3vQb9VFW0qkX1b2gkYFDXKmxVxzpM4xb5BZ8FQiqMxZRHUDDqFLXXMXFd32xag8hmqughuG570pHJWY0ascBDSMqVHGBaKqghuEhE0DD8JAJoGF4yATQMDxkAmgYHjIBNAwPmQAahodMAA3DQyaAhuEhE0DD8ND/B5R/++21JqdXAAAAAElFTkSuQmCC)
Maths-General
Maths-
Use △ ABC, where M, N, Q are midpoints of the sides.
MN = 3x + 8, BC = 2x + 24
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPQAAAC/CAYAAADJsPFRAAAgAElEQVR4nO29eXwUVbr//z5VvWRj30F2lACygyJuMCBkQDAsIRACJAEcFL1z9c53lnu9M97ffd3f947OuKCjiCQhC0lgJgEEEQGVTZR9EWQRUBZhZIfs3V11vn90V9EBRdCE9FJvX2036eruqlPnc55znvOc5wgppcTCwiIkUGr7BCwsLKoPS9AWFiGEJWgLixDCErSFRQhhCdrCIoSw1fYJWFQ3/pMWotbOwqJ2sAQdwEhAIH0SFdf+76dZKSUI0KVA4kEoLt8BDhRpR1iaDissQQc4uu/5e3UpAelG1xR0YUMXAgUPoCGw+RoEi3DCEnTAcxNJCh23p5zi4jJKywQNmzTCqUYCHrzuER3LTRJeWHc7qJCADkLzPeDSxTM8+WQav/jFL9i5cy827IDTe7jQqDqmtgh1LEEHOFKCNP6TEil1PB4XmuYGPBz48iDnzp+jbt1Itm3dSUmZREoFXZNIqZkjcIvwwBJ0MCAxDa0hal134yovZd26LfTu2Z/k5CTWrl3JmTOnvZ10AUhpjaHDDEvQQYEhSx2ERFFAVSUXL13g8817ePihxxjy2KOcPPUVX3yx23uoVAAFS9LhhSXoQEcYHW4vuq4DEoHg0MFDgJ1HHxnCPXffQ2yXu/l8y2ZclR4kAt26vWGHdccDGMO2SgFSePvdQtPQ3Rq6S2dRTj4d72mDW6/kysUS+ve+j3Vr13Dp4nkkAk3asCauwgthrYcObDQkOjoCUKVE6h6QkqOHDzH68SeIbtCY6Dr1EOi4Kis4evRr/ud//8zU1BR0KXEqwpJ0GGHNQwcRUoCuS2x2OxvWb8QZ4WTeu/OIio5BSImqCP7w7//OmjWrmZCUhNPhqO1TtrjDWF3uAEb6/i/w3ighQSgqZSWlfLh2LYOHDKN3n7507tyZzrH30OmezsSPeYJdO3fy5YEDCOvuhh3WLQ9gDCErvnkrKQSKauPY18exR0STOn0mHl1DlzpS10C6GDp0CN2738uRw4etrnYYYo2hAxzpG0V78QaMlJSWcvVKCS1aNEOoAiEkitQRSDQJp8+cQ3E4adyoMQ5rDB1WWIIOcG4QtC6QEoSi4PFo2OwCgeYVtJC4XB4UWwRu30cibDZL0GGE5RQLaCTXlkwp3hdSeueYNc08RAjhe09gtztxazo2xYa1djL8sCx0wGPcnmvilNetixQ3xGuL7/mURThgCdrCIoSwvNwWFiGENYYOcnRdR0qJEAIpJYqi+MbUFuGIJegQQEqJruuWkC2sLnew4119dQ1L1OGNJegg59ixY6xZswabzYaqqrV9Oha1jNXlDjKMMbOUEpfLxdy5c9m1axcdOnSgc+fO5njaIjyxLHQQYoj2q6++oqCggE8//ZSCggIqKiosMYc5lqCDDF3X0XUdt9vNiy++SP369Rk2bBjLli3j4MGDtX16FrWMJeggxOFw8N5777Fp0yaee+45/vjHP1JRUUFubi4VFRWAb0cNi7DDEnSAY4yXjYfNZuPcuXNkZmbSqVMnxo8fT9++fZkyZQqLFi3i888/B0DTNDRNs4QdZliCDnCEEFUeuq5TUFDA/v37+d3vfke9evVQVZX4+HiaN29Oeno6V69eBSwrHY5Ygg5wjDGzIc6jR4+Sm5vLQw89xJAhQ5BS4vF4uOeee0hJSWHt2rWsWLHCihgLUyxBBwGGMF0uFwUFBZw7d460tDRiYmIQQphd6ylTptC1a1fmz5/P5cuXqwjastbhgSXoIMAI69y1axf5+fmMGzeOBx980IwSczqdqKpK3bp1mT17NocOHSIzM9O07Jqmoes6mrGG2iJksQQdBAghKC8vp6ioCF3XSUxMJDIyskq32niOi4tjyJAhZGdnc+DAARRFsYJNwghL0EGAoihs2LCB3NxckpKS6Natm+n1vh6n08nMmTO5evUqhYWFuN1ucyWWJerQxxJ0AHK9WMvLy5k7dy4tW7Zk8uTJREZGVlk2eT19+vQhMTGR/Px8Nm/ejKqq5oosi9DGEnSAYQjPfx556dKlbNu2jZSUFDp27Ah4rbai3Hj7dF0nOjqaqVOnEhkZycKFCykpKbGcYmGCJegAw39MrCgKp0+f5o033qB3796kpKRUOe6HutBSStq3b09iYiLvvfceW7ZswWazWV3uMMASdIBhdLcNK7148WKOHTvGzJkziY6Ovmm32eiC67pOREQEiYmJ3HvvvbzxxhucP3/+ey26RWhh3eEAw7C8qqqyf/9+cnJyGDZsGIMGDbqlrCSGoHVdp0OHDiQlJbFt2zY2btxoOses7nfoYgk6wDAEp2kaBQUFlJSUMHv2bGJiYn5U0EZDYLfbzWQHTzzxBL179+Yvf/kLJ06cMCPLjLlpi9DCEnSAYSzA2LRpE4WFhUyYMIHu3bubYr4d66rrOo0aNeLZZ5/l66+/Ji8vD6gaH24RWliCDjAUReHKlStkZGQQFRXF5MmTiYqKqrLi6lYxut8PP/wwcXFxLFq0iD179pjTWFbXO/SwBF3LGA4w4wGwfft21qxZQ3JyMp07dzat809ZcCGlxOl08txzz1FRUUFmZqYZbGIReliCrmWMbrQh5jNnzvDyyy/TvXt3xo8fj81mQ1EU8/mnCFpKSWxsLOPGjWPFihV89tln1mqsEMUSdC1jCNkQ3qpVq9i9ezepqam0a9fuZzmujC61EAKbzcbkyZNp0KAB7777LlevXrUEHYJYgq5lDFEpisLJkyeZN28e999/PyNGjPjZY1z/pAgAnTt3ZtasWXzyySesXbv2Z5+7ReBhCTpAkFKSmZnJd999xzPPPEP9+vV/9m4YxrjbiBJTFIURI0bQrVs35s+fz5kzZ8wpMo/HYznJQgBL0AGAqqocPHiQJUuWMHz4cB5++GE0TauWLvH1U1QtW7ZkxowZ7N27l8LCQlPIVvc7NLAEXcsIIaisrOT111/H5XIxc+ZMIiIigBtXXf1cjBVacXFx3HfffWRlZXHmzBkURcHj8ViBJiGAJehaxBDrhg0bWLVqFcnJyfTq1atGs3VWVlZSp04dZs6cyYULF0hPT6eysvIHV29ZBBfWHawF/NcyX758mezsbJo1a0ZCQgLgdZCpqlrt0VxCCBwOB5qmMWTIEOLj48nJyWH//v2AlXcsFLAEfYe5PtHA0qVL+eijj3jmmWfMtc6GkKt7rth/PO1wOEhKSsLhcJCeno7L5aq237GoPSxB32H8re63337LwoUL6d69O3FxcWZI5p34fSklPXr0YNq0aXzwwQd88sknVpc7BLDu4B3Gf+fIZcuWceDAAVJTU2nevHmNO6X8w0s1TcNms5GcnEzDhg3Jy8uznGIhgCXoWkBVVU6ePEl6ejpxcXGMGTMG+OG0QtWF8f3GGB2801izZ8/mk08+YcGCBQB4PB5cLpcl8CDEEvQdRgiB2+0mNzeXK1euMGnSJJxOp/leTc8HX5/iCLxrpvv27cuCBQs4efKkGYhizU0HH5aga4GdO3eyYMECxowZw0MPPVRr52GkOapXrx5paWkcO3aMJUuW4HK5TAtuEVxYgr5D+AeJpKen43A4mDJlimmdawtVVbHZbAwbNoyRI0cyf/58Dhw4YKUrClIsQd8BjFhpIQQrVqzgww8/ZPr06cTGxtZqDLX/fHdMTAzTpk2jtLSUxYsX43K5zC63vzPNIrCxBH0H0DQNVVU5f/48b7/9Ni1atCA1NTXg1iT369ePMWPGkJeXx549e6qMoy1LHRxYgr4DGFZwxYoVbN++naeffpp69eqZXdpAEbXD4SAtLY0mTZowZ84cXC6XeX6Bco4WN8cSdA3hnwNMVVWOHDlCZmYmDz30EKNGjcJutwMEVDCHrut06dKFhIQE1q9fb6b+BSxBBwmBU5tCCGPMaaTKdbvdrFy5kuPHj/PUU0/RsGFDFEXBbrcHlKDBe+4TJ06kbdu2/Pd//zfnz58HqNEFIxbVR2DVphDCGB8LIdi/fz+ZmZmMHDmSfv361fap/SCGYO+66y7+5V/+hd27d1NYWGhZ6SDCEnQNYKT9MfZ1XrhwIZWVlUydOpX69esHpKXzzz8mpeSxxx5jyJAhZGVlceDAAWw2Wy2focWtYAm6BjBWVAkh2L17N++99565g4WmabV9et+LETlmbBDfoEEDfve733HmzBkWLVqE2+0Grg0nArFRsrAEXSMY4igvL+ell16ibt26TJs2DZvNFtBCMLrURpRY165dGT58OP/4xz/Yt28fcG0ttxV0EphYgq4BdF1HVVU++ugjNm7cWCVhfjARExPD1KlTEUKQk5NDcXFxlZBQa0wdeFiCrkYMi6WqKt999x1z5syhS5cuJCYmBp2YwXs9/fr1Y8KECSxbtowvvviiSqCJZaEDD0vQ1YD/djYGBQUF7Nu3jxdffJHmzZujqmqVlLrBgK7rOBwOxo8fT7NmzXjppZe4cuXKDVlXLAIHS9DVwPUCPXz4MAUFBQwZMoSBAweaxwTanPOPYQi3S5cuTJ06lU2bNrFq1aoqMeAWgUVw1bAAxbDOiqJQUVHBggULOH/+PKmpqTidzoD1bP8Yqqqa1xYfH0+3bt2YO3cuxcXFlpgDFEvQ1YD/HO6XX37JkiVLePzxxxk4cKAp9GDEf4zcuHFj/u3f/o1Dhw4xb948a/wcoARnTQswhBCoqkpxcTHZ2dlEREQwadIkIiMjsdvtQVv5jesyhgsjR45k8ODBZGdnc+DAAQAzvNUaUwcGlqCrAcPju2XLFhYvXszEiRPp1atXFcsdjPin/TWu4Ve/+hUlJSVkZ2dTWlpqxqxbBAaWoKsBRVEoLS1l/vz5tG7dmvHjx+NwOEKusgsh6N+/P5MnT2b58uVs27YNu90etA1WKBLigpaADmi+Z+8r6fuzlL5/owEe8xiJ7vus8fmbd5mFEBQVFbF+/XqmT59Ox44dzdVJoVTZpZRERkaSmJiIw+GgsLCQkpISFEWp0nBJjHK99sr3BSA1JNIsYx2j1H33Rf5YaVvcDCGDdYB3AxJ0HSkEEgFINM2FQEdzl3Ph/HeUa5E0atWeSF3DqetU2gUVqg2HfgVZUczZsxeIim5J/UZ1URUbQkiEriOkHRQBfto0xo5CCC5evMj48eOJjIykqKiI6Oho7xmFkKD947d1XeeVV17h1VdfZd68eYwePfoG51+FDnjc4LnA2SsuNBy0rN8Qp+qhQqjorlLKiitwO6OoV6ceTiHQFTc2TUG3qShUKW6LWyR0LLS88Z9CCGw2B98cO8boEWO5v//DbPpsF0JVQZXoAhQkwu0h/Z0MOnToxZ/++Aoet4IQCtes9HXf7RcRJoQgKyuLr7/+mqeffpqIiAjTWoWKmKHqeNputzNhwgTuvvtu5s+fz4ULF773Wu12hYvnTzHmiTHEDY/ni31fgsOOardRWlzM//mXXzP33fkoNoFZ3FgW+ucQOoK+DoGvC4eOx+MGXeGuFi2Z++brXCmvxGXTUBSBU7q4+O0ZNq77nC5d7kHzgMctfd/w/YI0Kq+iKOzbt4+srCyGDRtGXFxcSFllf/yzgHo8Htq1a8e0adPYtm0bH3/88Q3HK0gUqaG5XURHR3G5+Ap5+QVcvlKMREVqOh5NQ1XtWAmDq4+QFTT+PWQJSAdjx47n8Jf72HvwIG7FhkeC8JSyef0GVBzEDfsloCClUuV7ELKKto0IqsrKShYtWkRlZaUZRBLK+beuv67ExEQefvhhXn75ZU6fPo2UEk3T0DQNRUqE0EH30KhhfYbFxfHZ51v4/LMt6IBQvCbZ/ErLLFcLoStohK/SCBRVwaVDz1696dyhLWvXrMGDitB1PGWlLF/xAf0HDKReg3pIXUMIv9ol+d6et6qqbNy4kaVLlzJp0iR69+5tzsWGjFviOox5aSPZQZ06dUhNTeXo0aMsXLjQFLOU0uzgCMCjexg0+FF69OxOQf5CLly+6O1iCwVd6v4/ACHaGN4pQljQVdEVqFevPhPHjebTT9bw9TeniLApHD54iNOXShg2+pd4tDKE8KBLD1VVXLWSCSEoLS0lLy8Ph8NBcnIyUVFRIdvdNvC/NsMaDx48mCFDhpCdnc3evXtxOBzeHowAEEhVwaNr1K9fl7Spk9m9Yxsb1n0MUiKERBGKz99RW1cVWoSNoN26C6nY6N+nF1p5Mds2b0fBzRtvvEWvhx6lbecOCOFBw41Qfjzq6dNPP2XlypUkJyfTtm1bgLDK5GGMqW02G3/6059wuVzk5OTg8Xi8MeASJDZ072gaj9tN//79eGzIL8jNWsDlyxcRQkGXMnwq4R0gdMpSGPOePiRI3TsPqqODquLWdVq1bUnvXvew/dONrP/kc3btP85jccNRpI70gKrqIAQ6Al0qPtOh4fa4Te/1pUuXePPNN+natSvjx483t7MxEgMGa+z27eCfsqhTp05MmjSJlStXsmHDBu/fdQ8CDZ0IpFBB6ig2lRlPplFy4Sz/WLwEW0QkSA034AJ032SVIqU1ZfUTCaGap4PwBisIKRBSoEvQ0dGEBxQVD4LIunUZPORBTh3bz8svz6XtPX3p2iUWmxQouh1dd6Hpwhf2oHpjIYQHXfeYkV8rV65kz549pKam0q5dOzRNM8eXhpj90/SE6sMQtNPpZMqUKdSrV4/09HQuXDiPQ9VButFkJFJXUHzhI/d0uZdRI+JYkJXLt2cvoOIN6XEJkEJBqiKUKuUdJ2TLzog6UlABBalrKEIgsNO/3/3Y7SoffbSaKckTadywAVKXKKrq/VCVGBKBQEFVvYkJvvnmG1577TX69evH2LFjAb53p8br46BD8eFPhw4dmDp1Khs3buTTTzeDUAFvkI9AoApvVdN0nYSECTRs1JDNn31KpDMCO6Dim0yQ0vsiPEYu1U4I5Wb1mzf291IjABvt27YjJsKGRNKi+V088ugjIOrQs1dXhARFtdOkWTMqdBWb8LZ0uq9WSSFQfBFo+fn5nDp1iueff57S0lKuXr0KBNYOGLWBEIL77ruP1q1bM3fuXPr07s5dd7XEbnPSsnkzIp0OAKQUtGnXgT+88AIv/PG/qF+3rrcxFQLh74i0+tw/iZAK/ZTmFIhhMTV03YPH46KkzENkZB0cDokiPFSWu9E8AmdUNFKAIjUqy8rRJUTExCBUBSGlt5JJDUWxsWfPXiZPnsz+/ftp0qQJTqfT3D0yZIrxJ2JY7bKyMsrLK3j7rTmkTJuKW4eS0nIio6OJcDhQ0BDouFxurpaUEhVVF5sxf49ERfNq2WfhLW6PEBI0eMP8r1lqr8Clb15ZRZfeGG+BBxBeL6vuPV4YQQ5GRJQQxrcggMqKSmY/8wyrV6/GbrdTVlZGWloaTZs2NcfQFrB+/XqWLVtG//79KMjPo3Wbtr7hioJEIvwWvgihIqVAQ/jumu57H4Ql6J9ECHW54UaXgLeaeJssn7VF8T6EjpQeb8WRvsojpfchDC+rMQaETzdv5pNPPiEtLY3Y2Fiee+452rRpw69+9as7eH2BzZEjR1i6dCmDBg3i5KlT5CzM5/e/+z1C6N61LYrAGxRqrMLSAAUFBSGFMYiu3YsIckJM0FDVm+KLyTYqi9TxRRl7PeJCIqQOUvV18659UqAj8a76uXDpInPfmUuTJk1ISkqiWbNm5OfnM3/+fAYNGmTm3A71wJIfQgiBpmnk5eVx9OhRsrKyWPnBKvLy8ol/Ip6ePbqjaR6EWd18XkcJSGlK3Fg7KYVlm38qIejJ8fNPmx5Z47Vy7TUqAhtCqN4wRAW/0EOBroPum3des3oNn27axFNPPUWnTp2oV68ezzzzDMePHyc7O5uysjLz94wRjDGlE6oPY/8uI9Rzz5495OfnM3z4cB544AFSpk3FYbPx1lt/o7SsFEVVq0x5Cal4y16oIIyN/bz/tiaufjohWnLC72E8CRCK90mAQEH4prSqHO77iK5751lPnDjB/HffpWfPXgwbNsz0Zg8YMIDRo0ezePFiDh48iBDCdJCFg5U2Qj+FEFRUVDB37lxUVWX27NlERUXRvXt3pqVMY/ny5WzYsNG3HNUXTad7e0reshd+5e7tknvvS+iXYU0QooL++SiKgtvtprCwkMOHDzNjxgxatGhhJjaIiYkhKSkJgOzsbIqLi03rFQ74W+pt27axevVqxo0bx7333mta7bFjx9KqVSuysrIoLS01PxcODV5tER617xbxd/grisLJkyfJzc3l4YcfZsiQIeYxxnEPPvggCQkJFBUVsXPnzrARM1zLxlJcXMzLL79M8+bNmTRpkrk4Q9M02rZty7PPPsvmzZtZvHgxiqKYWV4saobwqYE/gpGK1nBuVVRUkJmZydWrV5k2bRr16tVDSomqqmYCeqfTyaRJk6hbty4ZGRmUlZWF1Zy0zWbj/fff57PPPmP69OnExsaafzd21xg5ciS9evUiOzubU6dOofrG0paoawZL0D6MtcxGbqwvvviC3Nxc4uPjTet8fcijpml06dKFKVOmsGrVKt577z2zwoY6QghOnDhBeno6vXr1YsyYMTcco2kajRo1YsaMGRw9epTFixfj8XiA0F0zXttYgvbhv6tiSUkJ77zzDnXr1iU5OfmmIrXZbOZ2senp6Vy+fPl7Y7tDDSklOTk5HD58mN///vc0adLkB48bOnQojz/+OLm5uRw5ciSshiZ3GqtkfRjTMHa7nbVr17Jq1SpSUlLo2rXrDbm1/cWtaRotWrQgNTWVPXv2kJOT873HhQrGNe3fv5+///3vDB06lIEDB/7gtXo8HqKiokhMTKSkpISFCxdSWVlZpQG1qD4sQfvhn4mkdevWTJw40dz+1b+r7b9U0rDGY8eO5f777ycrK4sjR44A11L9hkKllVLidnvXhJeVlZGbm2uGv0ZHR99wjUbZGOmKBg4cSHx8PDk5OezcudNMNujxeEJqM4LaxhK0H6qqkp+fz+bNm3nqqado1qzZTfds8hd5vXr1mD17Nl9//TVFRUXmWBFCxwoZDsFdu3ZRWFjIxIkTGTBgwE2vzygju93O1KlTqVevHu+++y4ul8tcU21RfVil6UNRFI4dO8b8+fO5//77eeKJJ27LEyuEYODAgYwaNYrc3Fy2b98eUtM0Ri/l8uXLZGRkUKdOHcaNG4fD4bilxSkej4fY2FgmT57M2rVrzUUuEDoNXiAQtoI25kqNaSaXy8Xy5cs5deoUaWlp5jTVrYjRiGWuX78+Tz75JKWlpRQWFlJWVoaiKEFbYf1DNY0pvXXr1rFixQqSk5Pp0aPHLVtZo0FITU2lc+fOvPbaa2aC/lBo8AKFsBU0XMuvDbB3714yMjKIj4/n0UcfBarGY//Y9xjPPXr0IC4ujkWLFrF79+6gtdDGGNe/4dN1nTfffJP27dszbtw487p+LPrLaBillDRp0oTU1FT27t1LUVGR2YsJ1kYv0AhrQRvWoaSkhL///e+UlZUxceJEYmJizPdvB03TiImJIS0tjQYNGjB37lxcLldNnHqNY5SN0SCpqkpWVhYHDhxg9uzZtGnTxjzuVr7LwOPxMGLECAYPHkxGRgaHDh2ydrCsRsJW0P6blO/atYuFCxeSkJDA/fffb1qmW8WwQEai+b59+5KYmMgHH3zAzp07g7qyGj2UY8eO8frrr/PAAw+QnJx8W99hrrDyNRINGjTg+eef5+TJkyxZssSyztVI2AoavKJ2u928/fbbtGzZkrS0NGw2221XMKNLbrfbzTGzsZnbf/7nf3LhwgWz63ozr3mgYXSTPR4PCxYs4Pz58zz99NPA7TmyjJS//imOY2NjGT16NLm5uWzdutU8NtjKKNAIa0E7nU7WrFnDpk2bmDx5MnfffTcej+e2HTX+OaqNbmqnTp2YPn06u3btYsmSJTesHw4WVFVl+/btFBYWkpCQwAMPPGCW0e3gX0YA9evXJzU1FU3TyM3NpaSk5AZHpcXtE7aCVlWVs2fP8tJLLxEbG8vEiRPRNM0MGPk5FcqwamPGjOHee+8lNzeXY8eOmYsWgqULrigKxcXF5OXlATBjxgwiIyOrJHL4qWiaRq9evRg3bhwffPABO3bsQNd1c4veYCmjQCNsBQ3wj3/8g4MHD/Lss8/SrFkzcxxcHauBpJQ0atSIF198kYMHD5Kfnx+UgRTr1q1jyZIlJCUl0aFDB3PFWXVgxME3b96cuXPnUlJSAmBZ6J9BcNWun4H/NAzAgQMHyMrK4pFHHjGnqfxDOn8OhiUGzLXU+fn57NmzJ6Atj+FTMMrp0qVLpKen07p1axITE4mJifnBRPu3izEEiY2NJTk5mTVr1vDRRx+Z3xvI5RTIhJWgja5ieXk5OTk5fPfdd/z2t78lJibGfL+6usRG19HpdJKWlsbVq1fJy8ujuLi4Gq6mZjGGHB9//DFbt24lKSmJ9u3bA1Sb4PwDVkaOHEmPHj147bXXOHfuXND1YgKJsCo5o8u7e/dulixZQnx8PLGxsTW+4H7AgAEkJCSwdOlS9uzZU2O/U52cOnWKv/zlL/Tv35+xY8dWu8iM8tY0jZYtW/L8889z7NgxFi1aZFnnn0HYCNqoJKWlpeTk5OBwOJgyZQpRUVE1Pk0SHR1NQkICqqqSk5NjZgkNNIxyUBSFxYsXc/jwYVJSUmjVqlW1e+f9N7wDGDp0KA899BALFizg4MGD1fY74UZYCVoIwc6dO1m9ejUTJ06kT58+5ri5JkWt6zq9e/cmKSmJoqIiPvnkE3PZYKDNuRrZWrKyshg6dChDhw5F07Rq984bSysNn4XD4eBf//VfOX/+PBkZGVRUVADcdpBPuBM2gpZSUlpayquvvkrTpk1JSEioEuhQkxj5x5KSkmjTpg1vv/02JSUlVaLVAgEj02l6ejqlpaW88MILxMTE1Ng5+o/HXS4XvXv3ZurUqRQVFbFjxw4Aa730bRI2ghZCsHLlStavX8+MGTPo1KkTHo/HzCFWk+M2IQRut5sOHbIqmYQAABTISURBVDowceJEtm7dyooVKwIu7a+iKHz66acsX76chIQEunXrZs7N1+QCCiklDocDVVVJSEggJiaGvLw8rly5YkbfWdwaIV1S/qupLly4wNy5c+nZsyejRo0y51OrI0jiVjAajNTUVHr06MFbb73Ft99+W+WY2lh15P97ly9fZt68edSpU4eUlJQqkW93IthDURS6detGSkoKK1euZOPGjTeco8XNCWlBG2NUXddJT0/n8OHDPP/88zRu3NispP4hmzWFoihmKqPGjRszY8YMDh8+TGFhIXCt4bnTY2rjd43sKuvXr2fDhg0kJyfToUMHs3z859VrAv+5bZvNRnx8PC1atCAjI4MrV65YFvo2COmSMirIvn37yM7O5pe//CXDhw+vkh7oTp2H/3NcXByDBw8mOzubvXv33lEreD1SSmw2GydOnGDu3Ll0796dsWPHmotU7lSgh/+1t2vXjunTp7N161bee++9gPIzBDohK2ijm1ZeXk5ubi6lpaXMnDkTuDG/9p0+r/r16/PrX/+a8+fPU1BQgNvtrpUsmP7JF5YvX86OHTt48sknad++fa0nw09ISOC+++7jb3/7GxcuXKi18wg2QkrQ/plD4JqTZ8mSJaSkpNCjRw+gdgUN16axRo8eTVFREZ999pkZH32nx4vGWuesrCwefPBBBg0aVCWqrjaQUlK3bl3S0tL49ttvycrKMv9uWeubEzKCvn69sZGSt7CwkMjISCZMmEBUVBR2u910htUm0dHRTJs2DbfbzYIFCygrK7vj52V43zMzMzl9+jQzZsygcePGVd6vLTRNY8SIEcTFxZGens6uXbvM87WcZD9MyAgauKHbunr1apYuXcq0adPo1KlTbZ5aFQxHXY8ePUhMTGTlypXs2LHjjgtIURQOHTpEQUEBo0aNYsSIEeZ7td3gGSvfnnnmGXPYVFlZGTZbDf1UQk7QRjjhlStXmDdvHvfccw/jx483U8YGCpqmERERweTJk2nVqhVz5szh7Nmzd9SjawTaKIpCampqFecc1O50kfHbXbt2Zdo07z7TH3/8cY173IOdkCoZIz7Y4/GwbNky9u3bR0pKCq1btw6osZexq4SmaXTv3p3p06ezbt061qxZYx7jvxNmdWGMQY3vXLduHStXriQlJYW+ffve4NWuLSvtP40VERHBzJkzqV+/PgsWLDAdZP6rtSyuETKCNqyLlJKTJ0/y17/+lYEDBzJhwoRa7z764z/3bTjCRo8eTfv27UlPT+fs2bM1WkmN6LirV6+Snp5O06ZNSUpKumHqrLbLzL98WrVqRVJSEuvWrWPdunUAZkJGS9RVCRlBG04xgEWLFnH69Glz36VAD/C/6667mDVrFl9++SUFBQXAtZVP1W2hDaHk5+ezdetWnnvuOVq1ahWQ2VT8837Hx8fTt29f0tPT+ec//2kGAwXiedcmIVUSTqeTvXv3kpuby8iRIxk0aJA5x1vbFudmSCkZO3Ys/fr1IzMzk+PHj5uBHdXdENlsNk6dOkVeXh733nsvo0aNMsURyGXUrl07pk6dys6dO1m7dq1ZLoF8zrVBUAvaf6sWgIqKCjIzM9F1nT/84Q84HA7gx3d2qE2MLmOdOnV4+umnOXfuHPPnz6+2FUb+ZWSspsrPz+fw4cM89dRTNGjQoMpWN4GIcW7Dhg1j8ODBvPLKKxw9etS00IF63rVB0Ar6+koohGD9+vWsWrWKyZMn07FjRxRFMVfrBKqg/XeoeOSRRxg5ciQLFy5kx44d1bJO+3orf+jQITIyMhg9ejSPPfaYuaNkoHuPdV2nYcOGzJo1i7Nnz5KXl2cKOlDvbW0QuHfwFjFu6IULF0wnj7Gvc7ARGRnJlClTkFKSn59PZWXlz5puM4RsNArl5eXk5eVRUVFhZmsJBoxGT9M0HnjgAXPvMCPYxOIaQSvo68d8mzZtYtOmTUyZMoV27doFzQZo/uGquq7Tp08fpk+fTn5+fpVprJ+D0UPZsmULeXl5TJgwgf79+wdF+UDVYYPD4eA3v/kNiqLwt7/9DZfLZYnaj6AVtFEZVVXl+PHjvPrqq/Tt25fHH38cRVGCJsuF0TAZIanR0dEkJibStGlTCgoKuHz5sunB/ymrxIypnZKSEt555x0aNGhAamoqTqczaARteOaNIYixz/SHH37Ihg0bAO91ut3uoGnIa4qgFTSA2+1G0zRWrFjBwYMHmTFjBnfddVeVHRiCAUPUxhj27rvvJjk5mY8//pgPP/ywSgW93TG1kZL3ww8/ZOPGjUyaNImOHTve8SWkPxf/MtI0jfHjx9O6dWveeecdTp8+XesLSgKFoBa0zWbj6NGjZGRkmAnz/ceNwXhzDW/0hAkT6NatGxkZGXz33Xc/OV2REIKLFy8yZ84cOnfuTHJycrXtfFFbSClp3749zz77LDt27GDlypXVsoVRKBC0gjY8w5mZmVy5csWcgglWIfujaRrt2rUjMTGRL774gpUrV5oryX7s2q5/30jJu3//fqZPn07Tpk3NLJ7BitEFHzp0KD179iQ/P5+TJ08G9TVVF0FVAka6HP/tbIqKinj88cd55JFHAMyxVjB1uf3xF+SIESPo1asXr732Gt98880tBX/4x2sLITh48CALFixg0KBBjBgxosoUVbAKwGjMjXROhw4doqioCI/HE9BTlHeCoLqj/nO2V65c4ZVXXiEyMpIZM2aY3chAiUX+qRjn7na7admyJU899RRnz55l4cKFt9xI+YeNLly4kHPnzvHb3/6W+vXrB3XZGPhHiQ0ZMoRhw4aRmZlpBpuEM0ElaGPqQlVV1q1bx+rVq0lJSaFr165B5+S5Gf4OnsGDBzN48GCysrI4dOjQLVloQ7SbN2+moKCA0aNH06NHj5CJqNI0zSyfmJgYpk6dSmlpKVlZWVRWVtb26dUqQSVoI+nfpUuXyM7Opn379sTHx4dktJDRE4mKiuL5559H13X++te/4na7gR9Ox2N4gi9fvkxWVhZOp5MZM2YQERER9L4FA//0y7quM2jQICZNmkReXp6ZoL8mFrcEA0ElaOPmLF68mM2bN/P0009z1113BcSC/OrCEKS/H6B3796MGzeOFStWmLmqfyj22hg/b9++3dzyp0uXLqZVCwWuX34K3qSCderUISMjg9LSUnPePlR6JbdKUAlaURSOHz9OQUEBAwYMIC4uDkVRQu6mXS88m81GSkoKkZGRZGZmcvbs2e8dTxvDkbNnz/LWW2/Rtm1bxo8fj8PhqPbN5gIFRVHweDzExsYyffp01q5dy+rVq2t8v7JAJagEbawU+vLLL5k5cyaNGjWq4iAJFQvkjzGc6Nq1K7/5zW9Ys2YNmzdvBr5/6aCUkrVr17J582amT59ObGxsyIdHGkOx5ORk2rZty7x587h69aq5uUE4EdCCvj7NzOHDh8nOziYxMZEhQ4b8rAiqYMLj8aCqKo899hidOnUiIyPDnHf1T1UkhOCf//wnb7/9Nj179mTYsGFVEgCEauU2Fm4Yq7H27t3LwoULwzLQJOAFbVTYsrIycnJykFKSmJiI0+k0W2bjEYoIIcyxYqdOnUhNTWXLli28//77uFwucwsdI3Y9OzubEydOMHv2bJo1a2aWUahv+maMq0eNGsWAAQN49913OXr0aNBHxd0uAX2H/bvR27dvp6CggDFjxtCvX7+Qtsjfh2FpfvnLX9KnTx+ysrK4dOlSlT2hvvrqK3Jychg8eLC5r3M4WCgjmETTNOrUqcOsWbM4f/48RUVFtX1qd5yAF7SUEpfLxbvvvkvDhg2ZOnVqUK0Uqk6klLRs2ZLU1FROnDjB/PnzAW+Frqys5PXXX6e8vJznnnsubMrIP5ec8e9HHnmEadOmsWDBArZu3VqLZ3fnqXZB+4ce+j/7Z2i8PnXQzb5LCMH777/Pxo0bSUtLIzY2NqwSw/lHvhm9lSeeeILHHnuMd955h6+++gpFUdi0aRPLli0jOTmZnj17hk0P5vosqkIInE4niYmJaJpGTk4OpaWlpvBvpc5dn+7Yv74GeiNZ7aowxrzGPKDRevoXkn8K1pshpeT8+fNVVgpd/36oP4zy9C9Xp9PJtGnTzJ7LxYsXyc3NpW7duiQmJnpvrF+DV9vXUNOP669R0zS6dOlizt1//vnnZgP3Y/XO+Lz/s9FTDHQxA9SIJ8mIclIUIziiagUzghy8x/xwm6IoCoWFhRw/fpw333yT+vXrm98fLvzQtT766KOkpqayaNEiSkpK2Lx5M//xH/9Bt27dzGPCzSFkYATlzJo1i88//5x33nmH/v37ExkZCfx4/fF3sBpCDpY6V+2C9k/YXlJylePHT1BaWgpAnTp16NixI5GRkbdUSF9++SUZGRm0adOGmJgYtm/fXt2nG3R4LY1EUVT69OlDRkYGWQsW0KVLF6Kjo9m5cydut8fXRZdAaM7P3wzDkgoh6NKlC4sXL2bNmjXEx8f/6Gd1Xefw4cNcvnyZZs2a0aZNmyr7aQV6WQpZzf0Iqel4pI7dJti8fjXTZv4WR4SduhEqjqhIBg96jKkpqbRq3QoVDZvi65JjR0eAz2prmsaf//xnXnzxRTMDSbiMC2+GTVHR8VUuRSAluF2uKpFj3sYS3+vaOtPaxV94Ho+HAQMGUFhYSLOmzVAVFSlAFyCkG3Q3iiL45sQplhQtZ0nRexQXF9O6TRt+GTecMWPG0Lx5M2+5KoEt6OrvcgsF7zV70CovEhXTkBf+v/+kT6dW7P1yH3/6rz+jqxH82++eJ9IG4F1soAsVXargG2cXFxfTp08f3nrrrbAMEDDQhUR4XyAkCARSSKQAiY4QKkIoCCTSbPCk7wEBPpFR4/j3BN1ut7dYdB1dKOiKRMGDSgUnvjnBC3/8H86evcqsWb+i09138/Wxr1m1ahV339OZ5i2aoWk6qgjs9dY1MoY2qpIQCqrdRsdOHekY257WHduzuHAZ3546gcftAZsKQgGpI5AgpSne6Ohohg0bFrbjQIvqx+1xg9SQQgEhQEgUBKCwYvkq9u8/whtvvM1DDw5ASrjvvn48MuhhbKodj0cnGIYvNRpeJX3/K75STGVxMbv27ebc2X/y+MCHsDls6AJAeB9SIKRA1zVzKsLw8oYzugQdUJC+B0ihIBQFj5TobheALwuJiqZ7K56BIDx7NgaGt1pRFBShADoIHRSBwNv7Kb58lc82b6d7j350797TzIwjhKBxo8a+4YseFIn9q1/QXj8MIBFILl+6xLNPP0WTKMHpc/9kwAMDGD7sMYQi0KSOjooivQ2mIkD49nQK5EK7U/h3moUEIbyNm657OHniDP9Ysoz3lxbisKsMGz6cseMm0LxlC1SbHbem4bTbUcK8HP2zqZp/w7fbCoDUKb5SwtnvLtDzvh5ERkWgKMLXQAo0TQ+qulj9Xm7/1xKiIiOYmppGt3ZNuVJ8mby8hfzxjy/wP399jZbNmyB94kc3gigC35N4JzFKQgjvsETzuCksWsqrr71F46YtmJCQgOapZNWHq1mYV8D//d8/8+gvfmFaa5vNGrJURcHrgFAQQgMh0N0uysorQFF8Ti+JohjecomUutdPYfYoA5ea7XILsDsiGDT4Efp16wRIGjWI4f/8+3/x5YFDtGjRDOkz6SLAC6r2ESBUThw/wpw33qBX777870t/pV6MAxBMmDSJJ5+cxeuvz6Hf/QOIjqmDsLR8I1KgSW/dFJoERSembl1aNG/Gd+fOUlFRiT3KCXhnCq5NWRkr2gLbyVj9oZ+mLgW6VBFComsa+MbCderUQVUVdI/b++O+1jLQW77awCgRifSO+5Bs2bIFJCRPSSYyIgJ3ZSXu8hKaNm7MjOmpHDl2lAOHDoHqndIK7xH0jXj9OuJaweiSeg0a0KtPD/bs3sGRI0d8byiAwuUrF7l69TK6NMeSAU0NNDcSXfOAVJG2BiiUo5Vfxa3pHDt2jLfmZtK4URN63NMRu67jnXBRkcI7HWNRFSk0NCpBesDj5uTXJ2jaqAmtWrQCG0ib3TtToLvo1eteHFERfHXyFB4BuhLuLrEbEUKiKDqq0LzTq8KOcEYydtwTtGwcw7NPzyI7O5evvjpGdvZCkiZNY9PGz1AVO1IPbOsMNdDllkhv91moqM5oPO4Knp71KxwOB5GRkXTp0oUXnpxFm1YtUaSOQA2Ghq9W8Vpo7yuPx43D5kBRbCh45+9Vuw30SpwOG6qqUlJW6vug5Vz8PqpMrugKUmrcE9uF////vkh2TgFz5sxhzpw3aNy4EUOHDqVX7z7oenD0dmok9FMIgcvlok/v3nz22WfmFJSUErvdboaHWvw43nrnnS1FlTgjIrhaXEx5RTkAmtS9N1FROHv2LBVlZTRr2sz74eDoJd5hrisQIdE8OkLAvT168vLL/dB1cLs9VbbX0XVjt5HALtBq70OYc36+zdYdDgeqqpqv/Y+xuDlei6CgonhDOIWDuzt35vQ/v+Xggf3Y8IaCKqoNhOD9Fe8TFRVN7x49kJpESD3Aq18tIXzm2ffwCtf78Hq4Fex2G6rqraPeZ6+opQxsQ1TtFtqI7DKySBhzyv5xxtfHHVt8P94YJpBcc1f37teXu9q0Zs7rr1Onbj169+9HZeklPljyd7Kzckmb/a+0aNb0WhCK1e3+AbzTU0J4h4fGUFGo3iAnVbVVWZppeLsD3ctd/YszfuTrrMp1e3inQr1ebomGrmts27aNt996l5MnThNVrw6KXgmVZRz+6iiDho9i2syn6NO7BzbdE7R7fNUk8oZ/ySrv3HwK1bDsgYkl6EBH+spU6Oh4zJVnF85f5NSJM5y/fIkIh6B1s0ZcuXSV3/3n/3Dk+Gl+/ewzPDkjBafTXttXEFD4y/f7/mqEg/4wgT2OtgQd6Eiflfaz0EIIVMWON8Lb13nUKxHAme8uUbR0OTZVZeb0VBTVKm9/brTHXgQS6YuXF+a7wu8ooxzDTNAWNUnVKmj85fpXFjfnhyq8uOm7144IZCxBW1iEEIHtsrOwsLgtLEFbWIQQlqAtLEIIS9AWFiGEJWgLixDCErSFRQhhCdrCIoSwBG1hEUJYgrawCCEsQVtYhBCWoC0sQghL0BYWIYQlaAuLEOL/AVS3us4R4dIUAAAAAElFTkSuQmCC)
Use △ ABC, where M, N, Q are midpoints of the sides.
MN = 3x + 8, BC = 2x + 24
![](data:image/png;base64,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)
Maths-General
Maths-
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex.
Right triangle: leg lengths are a and b.
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex.
Right triangle: leg lengths are a and b.
Maths-General
Maths-
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex.
Rectangle: length is l and width is b.
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex.
Rectangle: length is l and width is b.
Maths-General
Maths-
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex.
Square: side length is 4.
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex.
Square: side length is 4.
Maths-General
Maths-
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Isosceles right triangle: leg length is 5 units.
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Isosceles right triangle: leg length is 5 units.
Maths-General
Maths-
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex. Right triangle: leg lengths are 3 units and 4 units.
Place the figure in a coordinate plane in a convenient way.
Assign coordinates to each vertex. Right triangle: leg lengths are 3 units and 4 units.
Maths-General
Maths-
Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation T = 15n +2 represents the total amount T , in dollars, Salim will pay for tickets. What does 12 represent in the equation?
Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation T = 15n +2 represents the total amount T , in dollars, Salim will pay for tickets. What does 12 represent in the equation?
Maths-General
Maths-
In △ PQR, DE is the midsegment.
Find the value of x and the length of side PQ.
![](data:image/png;base64,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)
In △ PQR, DE is the midsegment.
Find the value of x and the length of side PQ.
![](data:image/png;base64,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)
Maths-General
Maths-
In△ ABC, AN = BN, BM = MC
Find AC.
![](data:image/png;base64,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)
In△ ABC, AN = BN, BM = MC
Find AC.
![](data:image/png;base64,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)
Maths-General
Maths-
The segment connecting the midpoints of two sides of a
triangle is
The segment connecting the midpoints of two sides of a
triangle is
Maths-General
Maths-
The segment connecting the midpoints of two sides of a
triangle is
The segment connecting the midpoints of two sides of a
triangle is
Maths-General
Maths-
Every triangle has ___ mid-segments.
Every triangle has ___ mid-segments.
Maths-General