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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.
Solution
Given: Two tangents PQ and PR are drawn from an external point to a circle with centre O.
To Prove: QORP is a cyclic quadrilateral.
Proof: Since, PR and PQ are tangents.
So, OR ⊥ PR and OQ ⊥ PQ ...[Since, if we drawn a line from centre of a circle to its tangent line. Then, the line always perpendicular to the tangent line]
∴ ∠ORP = ∠OQP = 90°
Hence, ∠ORP + ∠OQP = 180°
So, QOPR is cyclic quadrilateral. ...[If sum of opposite angles is quadrilateral in 180°, then the quadrilateral is cyclic]
Hence proved.
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