Question

Calculate the length of tangent from a point $15cm$ away from the circle of a circle of radius $9cm$.

Answer 1

We know that tangent to a circle makes a right angle with radius.
$$\angle OPQ={90}^{\circ }$$
Applying Pythagoras
$$\begin{array}{cc}& {OQ}^2={OP}^2+{PQ}^2\\ & {15}^2=9^2+{PQ}^2\\ & {PQ}^2=225-81\\ & {PQ}^2=144\\ & PQ=\sqrt{144}cm=12cm\end{array}$$
Length of tangent = 12 cm