Question

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. Find the length of PQ.

Answer 1

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
$\therefore OP\perp PQ$
By Pythagoras theorem in $\Delta$ OPQ,
$O{Q}^2=O{P}^2+P{Q}^2\Rightarrow (12{)}^2=5^2+P{Q}^2\Rightarrow P{Q}^2=144-25\Rightarrow P{Q}^2=119\Rightarrow PQ=\sqrt{119}cm$