Maths-
General
Easy

Question

In the given figure, A B is the diameter of the circle, centered at ´ O to the power of ´ end exponent. If angle C O A equals 60 degree comma blank A B equals 2 r comma blank A C equals d blankandblank C D equals l comma then l is equal to

  1. d square root of 3  
  2. d divided by square root of 3  
  3. 3 d  
  4. square root of 3 d divided by 2  

The correct answer is: d square root of 3


    A C equals d comma blank O A equals O B equals r comma blank C D equals B D equals l comma blank angle C O A equals fraction numerator pi over denominator 3 end fraction
    therefore A C to the power of 2 end exponent equals O A to the power of 2 end exponent plus O C to the power of 2 end exponent minus 2 blank A O blank O C cos invisible function application fraction numerator pi over denominator 3 end fraction
    rightwards double arrow d to the power of 2 end exponent equals 2 r to the power of 2 end exponent minus 2 r to the power of 2 end exponent fraction numerator 1 over denominator 2 end fraction equals r to the power of 2 end exponent

    Also, angle B O D equals angle C O D equals fraction numerator 2 pi over denominator 3 cross times 2 end fraction equals fraction numerator pi over denominator 3 end fraction blank rightwards double arrow tan invisible function application fraction numerator pi over denominator 3 end fraction equals fraction numerator B D over denominator O B end fraction equals fraction numerator l over denominator r end fraction rightwards double arrow l equals r square root of 3 equals d square root of 3

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