Question

In the following figure, $PQ$ is a chord of a circle with centre $O$ and $PT$ is a tangent. If $\angle$ $QPT$ = ${60}^o$, find $\angle$ $PRQ$.

Answer 1

Given, PQ is a chord of a circle with center $O$. Also, ∠$QPT$ = 60°.

let $x$ be the point on the tangent $PT$.

Now, $\angle QPT+\angle QPX$ = $180°$ [Linear pair]

$\Rightarrow \angle QPX=180°-\angle QPT$= $180°-60°$ =$120°$

Again,$\angle QPX$=$\angle PRQ$ [$\because$ Alternate segment theorem]

⇒ $\angle PRQ$= $120°$