Q. 24.8( 23 Votes )

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

Answer :

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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