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AP EAMCET201921 Apr 2019Evening ShiftMathematicsProperties of TrianglesActual

Let a triangle A B C be inscribed in a circle of radius 2 units. If the 3 bisectors of the angles A , B and C are extended to cut the circle at A 1 , B 1 and C 1 respectively, then the value of A A 1 cos A 2 + B B 1 cos B 2 + C C 1 cos C 2 sin A + sin B + sin C 2 =

Options

  1. A4
  2. B16
  3. C25
  4. D1

Correct answer

B. 16

Step-by-step solution

Consider the figure below. The triangle A B C is equilateral. Therefore, A = B = C = 60 ° . Substitute the value in the given expression, A A 1 cos A 2 + B B 1 cos B 2 + C C 1 cos C 2 sin A + sin B + sin C 2 = 4 cos 60 ° 2 + 4 cos 60 ° 2 + 4 cos 60 ° 2 sin 60 ° + sin 60 ° + sin 60 ° 2 = 4 × 3 3 2 3 3 2 2 = 16

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