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NTA Abhyas JEE Main2020MathematicsCirclePractice

Let A 0,3 and B 0,12 be two vertices of a ∆ A B C where C = x , 0 . If the circumcircle of ∆ A B C touches the x -axis, then the value of cos 2 θ is (where, θ is angle A C B )

Options

  1. A1 3
  2. B1 2
  3. C8 15
  4. D7 25

Correct answer

D. 7 25

Step-by-step solution

O A × O B = O C 2 ⇒ 3 × 12 = x 2 ⇒ x = 6 Centre C ' = 6 , 15 2 ∠ A C ' B = 2 ∠ A C B = 2 θ ⇒ cos ⁡ 2 θ = 15 2 2 + 15 2 2 - 9 2 2 × 15 2 × 15 2 = 225 2 - 81 225 2 = 225 - 162 225 = 63 225 = 7 25

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