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Manipal MET2015MathematicsProperties of Triangles

If an isosceles triangle of vertical angle 2 is inscribed in a circle of radius a . Then, area of the triangle is maximum, when is equal to

Options

  1. A6
  2. B4
  3. C3
  4. D2

Correct answer

A. 6

Step-by-step solution

We have, A D=a+a 2 and B C=2 B D=2 a 2 Area of A B C is given by = 1 2 B C A D= 2 2 a^2( 2 + 2 2 ) =a^2 2 + 1 2 a^2 4 On differentiating both sides w.r.t. , we get d d =2 a^2 2 +2 a^2 4 For maximum or minimum, put d d =0 . array rlrl & 2 & =- 4 & & 2 & = -4 & & & = 6 array Now, d^2 d ^2 =-2 a^2 2 2-2 a^2 4 4=-4 a^2 2 -8 a^2 4 At = 6 , d^2 d ^2 =-4 a^2 3 -8 a^2 2 3 aligned & =-4 a^2 3 2 -8 a^2 3 2 & =-6 a^2 3 0 aligned Hence, is maximum for = 6 .

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