Two tangents PQ and PR are drawn
Question:

Two tangents PQ and PR are drawn from an external point to a circle with centre 0. Prove that QORP is a cyclic quadrilateral.

Solution:

Given Two tangents PQ and PR are drawn from an external point to a circle with centre 0.

To prove QORP is a cyclic quadrilateral. proof Since, $P R$ and $P Q$ are tangents.

So, $O R \perp P R$ and $O Q \perp P Q$

[since, if we drawn a line from centre of a circle to its tangent line. Then, the line always perpendicular to the tangent line]

$\therefore$ $\angle O R P=\angle O Q P=90^{\circ}$

Hence. $\angle O R P+\angle O Q P=180^{\circ}$

So, $Q O P R$ is cyclic quadrilateral.

[If sum of opposite angles is quadriateral in $180^{\circ}$, then the quadrilateral is cyclic]

Hence proved.