Question

A tangent $PQ$ at a point $P$ of a circle of radius $5cm$ meets a line through the centre $O$ so that $OQ=13cm.$ Find the length of $PQ.$

Answer 1

Since tangent at a point is perpendicular to the radius through that point. Therefore, $OP$ is perpendicular to $PQ$.

In right triangle $OPQ$, we have
${OQ}^2={OP}^2+{PQ}^2$ [Using Pythagoras theorem]

$\Rightarrow {13}^2=5^2+{PQ}^2$

$\Rightarrow {PQ}^2=169-25=144$

$\Rightarrow PQ=12cm$.