Question

$PQ$ and $PR$ are tangents to given circle as shown in the figure. If $\angle RPQ={90}^o$ and $PQ=8cm$, find the radius of the circle (in $cm$).

Answer 1

Given that: $\angle RPQ={90}^{\circ },PQ=8cm$

To find: Radius of the circle

Solution:

Since, $\angle RPQ={90}^{\circ }$

$PQ=PR=8cm$ (tangents from external point to the circle are equal.)

and $\angle PQO=\angle PRO={90}^{\circ }$ (tangents to the circle are perpendicular to the the radius of the circle.)

$\therefore PQOR$ is a square.

So, $PQ=OQ=OR=PR=8cm$

So, radius of the circle$=8cm.$