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: PQ and PR are two tangents drawn at points Q and R are drawn from an external point P.

To Prove: QORP is a cyclic Quadrilateral.

Proof: OR ⏊ PR and OQ ⏊PQ   ......[Tangent at a point on the circle is perpendicular to the radius through point of contact]

∠ORP = 90°

∠OQP = 90°

∠ORP + ∠OQP = 180°

Hence QOPR is a cyclic quadrilateral. As the sum of the opposite pairs of angle is 180°