Question

Two tangents pq and pr drawn from external point to a circle with centre o. Prove that qorp is a cyclic quad

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°

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