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Question

Question 3
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) 119 cm

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Solution

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
OPPQ
By Pythagoras theorem in Δ OPQ,
OQ2=OP2+PQ2(12)2=52+PQ2PQ2=14425PQ2=119PQ=119 cm

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