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NTA Abhyas JEE Main2020MathematicsCirclePractice

From a point P 3,3 on the circle x 2 + y 2 = 18 , two chords P Q and P R each of 2 units length are drawn on this circle. The value of cos ∠ Q P R is equal to

Options

  1. A1 3 2
  2. B- 8 9
  3. C2 3
  4. D- 4 9

Correct answer

B. - 8 9

Step-by-step solution

Let angle O P R = θ then in ∆ O P R, cos ⁡ θ = 2 2 + 3 2 2 - 3 2 2 2 × 2 × 3 2 ⇒ cos ⁡ θ = 1 3 2 Now, c o s ∠ Q P R = cos ⁡ 2 θ = 2 c o s 2 θ - 1 = 2 1 3 2 2 - 1 = 1 9 - 1 = - 8 9

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