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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Given : two tangents PQ and PR are drawn from an external point P to a circle with center O.
To Find : prove that QORP is a cyclic quadrilateral
Solution:
two tangents PQ and PR
Hence ∠OQP = ∠ORP = 90°
=> ∠OQP + ∠ORP = 180°
∠OQP and ∠ORP are opposite angles in QORP quadrilateral
=> if sum of opposite angles in Quadrilateral = 180° then quadrilateral is cyclic
Hence QORP quadrilateral is cyclic
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