Question

Question 2
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

Answer 1

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

To prove: QORP is a cyclic quadrilateral.
Proof:
Since PR and PQ are tangents.
So, OR $\perp$ PR and OQ $\perp$ PQ
[Since if we draw a line from centre of a circle to its tangent line, then, the line will be always perpendicular to the tangent line]
$\therefore \angle ORP=\angle OQP={90}^{\circ }$
Hence $\angle ORP+\angle OQP={180}^{\circ }$
So, QORP is cyclic quadrilateral
[If sum of opposite angles is quadrilateral in ${180}^{\circ }$, then the quadrilateral is cyclic]
Hence proved.