Two tangents PQ and PR are drawn from an external point P to a circle with centre O. Prove that QORP is a cyclic…

CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 2 Marks · July 2024 · Standard

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1122 Marks · July 2024 · Standard

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

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Sol.
PQ $\perp$ OQ $\Rightarrow \angle PQO = 90^{\circ}$
and PR $\perp$ OR $\Rightarrow \angle PRO = 90^{\circ}$
$\therefore \angle PQO + \angle PRO = 180^{\circ}$
Since opposite angles of quadrilateral QORP are supplementary, therefore QORP is a cyclic quadrilateral.