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 )

Question

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 ), 1 3, 1 2, 8 15, 7 25

MARKS App · Accepted Answer

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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