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) √119cm
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Solution
The line drawn from the centre of the circle to the tangent is perpendicular to the tangent. ∴OP⊥PQ By Pythagoras theorem in Δ OPQ, OQ2=OP2+PQ2⇒(12)2=52+PQ2⇒PQ2=144−25⇒PQ2=119⇒PQ=√119cm