Calculate the length (in $\text{cm}$) of $PQ$, if the radius of the circle is $7\text{cm}$ and the line through the centre $O$ meets the tangent at point $Q$ such that $OP=25\text{cm}$.

A line drawn from the center of a circle to a tangent line at the point of contact is perpendicular to the tangent. Therefore, $△OQP$ is a right-angled triangle at $Q$.In right-angled $△OQP$:Radius $OQ=7\text{cm}$ Hypotenuse $OP=25\text{cm}$ Using Pythagoras' theorem:
$$O{P}^2=O{Q}^2+P{Q}^2$$
$$25^2=7^2+P{Q}^2$$
$$625=49+P{Q}^2$$
$$P{Q}^2=625-49$$
$$P{Q}^2=576$$
$$PQ=\sqrt{576}=24\text{cm}$$