Maths-
General
Easy
Question
of an isosceles triangle ABC is acute in which AB = AC and BD
AC . Prove that
![B C squared equals 2 cross times A C cross times C D text . end text](data:image/png;base64,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)
![](data:image/png;base64,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)
The correct answer is: Hence proved
Solution :-
Aim :- prove ![B C squared equals 2 cross times A C cross times C D](data:image/png;base64,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)
Hint :- Using pythagoras theorem, find the length of side AB and BC .
Substitute the RHS of
in terms of AC and CD Explanation(proof
Using pythagoras theorem,in triangle BDC
![B C squared equals C D squared plus B D squared minus Eq 1](data:image/png;base64,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)
Using pythagoras theorem,in triangle BDA
![A B squared equals B D squared plus A D squared not stretchy rightwards double arrow B D squared equals A B squared minus A D squared minus Eq 2](data:image/png;base64,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)
Substitute Eq2 in Eq1
![B C squared equals A B squared minus A D squared plus C D squared](data:image/png;base64,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)
Substitute AD = AC - CD (from diagram)
![B C squared equals A B squared minus left parenthesis A C minus C D right parenthesis squared plus C D squared not stretchy rightwards double arrow B C squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARAAAAASCAYAAACTtYGqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABABJREFUeNrtWz1oFEEUXg4JIiJYiBwiQgiSKgSCSBCxCRJERAIiQSSIECQEsQiIWKQQIQSLIBIQCZLiEIJYBBEhpJAjXCMhWFgEgljaBJEgRwis75m3Og5zt/N2Z2dmz/ngK2532Tffe/Pe/O1FUXGIibvANWBPVA6Utd0BoT91pIYKcAK4XjKnlbXdIflCf+pIDc2SOq3IdmMwZkKd+O2Dif+kmDeDBj4uAD+U0FFFtrsP2Ai14w/WyCednHxlzQOWBgzSHvArcAu4DKwqnusGzgI3gD/p+UfAo9JzVeoc3RZF3tPoiGkai243vrvfgBZOLExC12ZTWIogd4BLwFPScwPAugfJZ1qXyzywnss99BIR+KKX0rUp4FvgeZpeIk5SZxefPU3PVS067TqtmQ/k0Fh0u/spEHm1cGJhEro2ZV9XyKeT1ElHpPfWqZC4Sr6idLnIAye5fBVYk66NSNfuA19oCEBD74BHLDoNK+Yn4AppyaLRRrtnqbPl1aIbC5Pg2FT5OsE14A+h0yLuKvaEsiZf7IkuF3ngLJen6aUiFoHDQjC3UkbEBGiw17LTngNHgWPAZxk12mj3e6r4ebRwYmEKXJvTNMK1Ak77zwi/B4Grhgah2BNdpvrTFNMPTnJ5iSpXhabZC9Ia/InmmjyS1odxSkBjDaZhkEYqxHFyThaNWWxzgSNUV04tnFiYAtcm+vpKm/tYLIaE313kGxODUOyJLlP96SEtj84x2mg9lzelTaFh6f7nyM+zeKyiH2ntlmC9RedL02gDewa0uIgF1+ZmytLjC/CYdG3XUDGPPdOVNVFVfCwt/bzI5QoZSkYCrKANmuok9309RlNNKdHJE0yNRQScW0B0tOSJRdY2c22KvlbhEPCb4vpuh+oyhQXSUvMtl89K60/EjWh/w081vTSJPEuY3kj9gREe+y0zNdpCqyWMrpYiY9EKXJsqX4sYU2zgmdQVe6TL9AxkJmUG4iSXR6m6ibgpOWOHKqxPqLdxtHwEqqPRBlZarGU5WlzEgmNT5WsReMLUp9j7WbVcQGzoMgHOHoiTXH4KvKWYLo1Kv6c8Kh7jwLk2918BLzE12oDqGJerxUUsODZVvk4w10LrpMHZYOyRLhPA9h32OZffCBstuAGE59kb0lQbv7LbBj6I/n6ldhB4mRo0ZLEzV6nat3PqbSmgOhptQP6QLIsWF7Hg2BR9nUybL0b7JyvzbWaTAw4KSNG6bMNJLm8L0+UmjXgnFM/hzu0iraHw2e/A19LoaANLJLYdsP2bGTTaQEOY6mbR4ioWujZFX+OmMW4s1miZokLap+xFoyhdLlC2XA7IgPBnun+h82e6gIAAAXei8Hf+ZE9oPLihfPgFPPMAS+xgq7sAAAGWdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPkI8L21pPjxtc3VwPjxtaT5DPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz49PC9tbz48bWk+QTwvbWk+PG1zdXA+PG1pPkI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW8+KDwvbW8+PG1pPkE8L21pPjxtaT5DPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5DPC9taT48bWk+RDwvbWk+PG1zdXA+PG1vPik8L21vPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5DPC9taT48bXN1cD48bWk+RDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3gyMUQyOzwvbW8+PG1pPkI8L21pPjxtc3VwPjxtaT5DPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbWF0aD7SVXLQAAAAAElFTkSuQmCC)
![equals A B squared minus A C squared minus C D squared plus 2 cross times A C cross times C D plus C D squared](data:image/png;base64,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)
![text As end text A B equals A C left parenthesis text given end text right parenthesis text we get, end text B C squared equals A C squared minus A C squared minus C D squared plus 2 cross times A C cross times C D plus C D squared](data:image/png;base64,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)
![not stretchy rightwards double arrow B C squared equals 2 cross times A C cross times C D](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
Convert the following fraction to decimal
a) 9/11
Convert the following fraction to decimal
a) 9/11
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
b) 0.743434343......
Express the following recurring decimals as vulgar fraction
b) 0.743434343......
Maths-General
Maths-
ABC is a triangle in which AB = AC. P is any point in its interior such
that
. Prove that AP bisects ![straight angle BAC](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC is a triangle in which AB = AC. P is any point in its interior such
that
. Prove that AP bisects ![straight angle BAC](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAOCAYAAAC/10U/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAZNJREFUeNrVlTFIw0AUhkMoIuJSHEQkCE4iIoUiDq4i4uDg5uDURRxcRcTJTToLDg5SJIs4ibhIESdBnEoRQYo4uTiIQ+mi/4O/cBwvd0nM0h8+2jte7v5c3nsXBPm1EgyoTkBszf2SD/ACrsCkY439FPtMgTpogx54BUdgLK/xU/AFFhXzpjbBY8IaFcbPOPZZB09gFYScmwA1cJvH+HmCcc18yNPS1ABnRNMseAPlolKl4TCumY/AsxIXMa0CpkOU8HV3ijJ+6TFumg9ZzPegqsTVDWPye6zEvHvqJZVCFp7PuFmwwieYU2JGmQ5DHJdAh/Omev81Xspg3Dx5MbYMrsG80mEOrTkZ7xVpvsTN0xrXcl46SdNaUyvCMltgaMwl1YJXcnI3GY1r5kVd4/+2lVo2NasudrMaH2YPzWo8qVX+GOMWmHZcRi2rI3XY11NpBNzlNG6bFzMHvBdEa+xYLsWM62uDL7BlFPg4xw/2w03PZ7WJHd2my3uhn9/SNhc85quKqQpf+pvrysFegKVg0PUHLolwiHYWAQMAAABxdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDIyMjA7PC9taT48bWk+QkFDPC9taT48L21hdGg+6cWE1wAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Maths-General
Maths-
Evaluate:
a−3b−4 / a−2b−3
Evaluate:
a−3b−4 / a−2b−3
Maths-General
Maths-
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,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)
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,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)
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Maths-General
Maths-
(32)3 + (2/3)0 + 35 × (1/3)4
(32)3 + (2/3)0 + 35 × (1/3)4
Maths-General
Maths-
Express 0.5248 in the lowest form.
Express 0.5248 in the lowest form.
Maths-General
Maths-
Write the following numbers in the scientific notation : 0.00000000065
Write the following numbers in the scientific notation : 0.00000000065
Maths-General
Maths-
Write the following numbers in the scientific notation : a) 5,07,460000000
Write the following numbers in the scientific notation : a) 5,07,460000000
Maths-General
Maths-
A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?
A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?
Maths-General
Maths-
The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?
The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?
Maths-General
Maths-
A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?
A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?
Maths-General
Maths-
Convert the following fractions to repeating decimals
d) ![1 over 6](data:image/png;base64,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)
Convert the following fractions to repeating decimals
d) ![1 over 6](data:image/png;base64,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)
Maths-General
Maths-
Convert the following fractions to repeating decimals
c) ![10 over 33](data:image/png;base64,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)
Convert the following fractions to repeating decimals
c) ![10 over 33](data:image/png;base64,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)
Maths-General