Let A B be a chord of length 12 of the circle x - 2 2 + y + 1 2 = 169 4 If tangents drawn to the circle at points A and B intersect at the point P , then five times the distance of point P from chord A B is equal to _____.

Step-by-step solution

Plotting the diagram of given value we have, Now given, radius = 169 4 = 13 2 Now by diagram M is the midpoint of A B so, A M = 6 Now in ∆ A M P , P M = 6 cot θ And in ∆ O A M sin 90 ° - θ = 6 13 2 ⇒ cos θ = 12 13 P M = 6 × 12 5 = 72 5 ⇒ 5 P M = 72