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 $OQ=12cm$. Length PQ is :
(A) 12 cm (B) 13 cm (C) 8.5 cm (D) $\sqrt{119}$cm.

Solution: We can draw a diagram with the given details. Please refer to video for the diagram.
We know tangent at any point $P$ is always perpendicular to line joining the center $O$ of that circle.
In other words, $OP$ is perpendicular to $PQ$.
It means $\Delta OPQ$ is a right angle triangle.
So, using pythagoras theorem,
$O{P}^2+P{Q}^2=O{Q}^2$
$5^2+P{Q}^2={12}^2\Rightarrow PQ=\sqrt{144-25}=\sqrt{119}cm$