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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