Q4 of 31 Page 233

P is in the exterior of a circle at distance 34 from the centre 0. A line through P touches the circle at Q. PQ = 16, find the diameter of the circle.

Given OP = 34, PQ = 16


OQ is the radius of the circle.


Since PQ is a tangent to the circle, OQ ⊥ PQ.



In right angled ΔOQP,


By Pythagoras Theorem,


⇒ OP2 = PQ2 + OQ2


⇒ 342 = 162 + OQ2


⇒ OQ2 = 1156 – 256


⇒ OQ2 = 900


⇒ OQ = 30


∴ Diameter of circle = 2r = 2 × OQ = 2 × 30 = 60


∴ Diameter = 60


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