Sum of Opposite Sides Are Equal in a Quadrilateral Circumscribing a Circle
Question 2 Tw...
Question
Question 2 Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
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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 draw a line from centre of a circle to its tangent line, then, the line will be always perpendicular to the tangent line] ∴∠ORP=∠OQP=90∘ Hence ∠ORP+∠OQP=180∘ So, QORP is cyclic quadrilateral [If sum of opposite angles is quadrilateral in 180∘, then the quadrilateral is cyclic] Hence proved.