Q9 of 31 Page 234

P is a point in the exterior of a circle having centre 0 and radius 24. OP = 25. A tangent from P touches the circle at Q. Find PQ.


Given P lies in the exterior of a circle having centre O and PQ is a tangent.


∴ OQ ⊥ PQ


Also given OP = 25 and OQ = 24.


Consider ΔOQP,


∠OQP = 90°


By Pythagoras Theorem,


⇒ OP2 = OQ2 + PQ2


⇒ 252 = 242 + PQ2


⇒ PQ2 = 625 – 576


= 49


∴ PQ = 7


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