Question

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 ⊥ PR and OQ ⊥ PQ   ...[Since, if we drawn a line from centre of a circle to its tangent line. Then, the line always perpendicular to the tangent line]

∴ ∠ORP = ∠OQP = 90°

Hence, ∠ORP + ∠OQP = 180°

So, QOPR is cyclic quadrilateral.   ...[If sum of opposite angles is quadrilateral in 180°, then the quadrilateral is cyclic]

Hence proved.