(Q10) A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q so that OQ = 12 cm. Find the length of PQ

Given : A circle with center O and radius OP=5cm

PQ is a tangent and OQ = 12 cm

PQO5cm12cm

We know that ∠OPQ = 90°

Hence in triangle OPQ

2=2+PQ2

[hypotenuse2 = Adj.side2+Opp.side2]

2 = 2+PQ2

PQ2 = -

PQ2 =

PQ = √