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 $OQ=13$ cm. Find the length of $PQ$.

Answer 1

Given,

$OQ=13cm$

$OP=5cm$

Using Pythagoras theorem, we have

$PQ=\sqrt{O{Q}^2-O{P}^2}$ [$\because$ Radius of the of circle is perpendicular to the tangent at the point of contact]

$=\sqrt{{13}^2-5^2}$

$=\sqrt{{12}^2}$

$=\left(12\right)cm$.