Question

In figure 2, PQ is a chord of a circle with centre O and PT is a tangent. if $\angle QPT={60}^0$, Find $\angle PRQ$.

Answer 1

From given figure: $PQ$ is a chord of a circle with centre O.

$PT$ is the tangent $\angle QPT={60}^{\circ }$.

Reframed the given figure based on given instructions and our requirement to find the unknown angle.

Take a point M on the alternate segment.

Join $MP$ and $MQ.$

$\angle MPQ=\angle QPT={60}^{\circ }$

[Angles in the alternate segment]

$\angle PMQ+\angle PRQ={180}^{\circ }$

[Oppsite angles of a cyclic quadrilateral]

So,

${60}^{\circ }+\angle PRQ={180}^{\circ }$

$\angle PRQ={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

Therefore measure of $\angle PRQ$ is ${120}^{\circ }$.