Question

If the length of tangent line is $4$ cm drawn from any point, $10$ cm away from the center of circle, then what will be the radius of that circle?

Answer 1

$PQ$ is the tangent drawn an circle from external point $Q$ and $OP$ is radius of circle.
So $\angle OPQ={90}^{\circ }$ (by theorem 13.1)
From $\Delta OPQ$
$O{Q}^2=P{Q}^2+O{P}^2$ (By Pythagoras theorem)
${10}^2=4^2+O{P}^2$
$O{P}^{=}{10}^2-4^2$
$=100-16$
$=84$
$OP=\sqrt{84}cm$
$OP=2\sqrt{84}cm$