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Question

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


Solution


Since tangent at a point to a circle is perpendicular to the radius through the point
OQQP&ORRP
OQP=90&ORP=90
OQP+ORP=90=180(i)
In quadrilateral, OQPR,
OQP+QPR+QOR+ORP=360
(QPR+QPR)+(OQP+ORP)=360 (From(i)
QPR+QOR=180(ii)
From(i)&(ii), we can say that quadrilateral QORP is cyclic

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