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AP EAMCET201921 Apr 2019Evening ShiftMathematicsProperties of TrianglesActual

If A B C D is a cyclic quadrilateral with A B = 6 , B C = 4 , C D = 5 , D A = 3 and ∠ A B C = θ , then cos θ =

Options

  1. A3 13
  2. B18 76
  3. C16 78
  4. D78 86

Correct answer

A. 3 13

Step-by-step solution

The figure below represents the quadrilateral. In triangle A B C , A C 2 = A B 2 + B C 2 - 2 ( A B ) ( A C ) cos θ ⇒ A C 2 = 6 2 + 4 2 - 2 × 6 × 4 × cos θ ⇒ A C 2 = 52 - 48 cos θ     . . . i Similarly, in triangle A D C , A C 2 = A D 2 + D C 2 - 2 × A D × D C cos 180 ° - θ ⇒ A C 2 = 3 2 + 5 2 + 2 × 3 × 5 × cos θ ⇒ A C 2 = 34 + 30 cos θ     . . . ii From equations i   &   ii , 52 - 48

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