Question

A line through the centre $O$ of a circle of radius $7cm$ cuts the tangent, at a point $P$ on the circle, at $Q$ such that $PQ=24cm.$ Find $OQ.$

Answer 1

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

In right triangle $OPQ$, we have
${OQ}^2={OP}^2+{PQ}^2$

$\Rightarrow {OQ}^2=7^2+{24}^2$

$\Rightarrow {OQ}^2=49+576$

$\Rightarrow {OQ}^2=625$

$\Rightarrow OQ=25cm$.