1. P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If ∠PSQ = 20°, ∠PRQ = ?
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- By: anil on 05 May 2019 01.57 am
It is given that $$angle$$PSQ = 20° and we know that $$angle$$OPS = $$angle$$OQS = 90° Now, in quadrilateral OPQS, sum of all angles is 360° => $$angle$$POQ + $$angle$$PSQ + $$angle$$OPS + $$angle$$OQS = 360° => $$angle$$POQ + 20° + 90° + 90° = 360° => $$angle$$POQ = 160° Using the property that angle subtended at the centre is double the angle subtended by the same points at any other point on the circle. => $$angle$$PTQ = $$frac{angle POQ}{2}$$ = 80° Also, PTQR is cyclic quadrilateral and thus sum of opposite angles is 180° => $$angle$$PRQ = 180° - $$angle$$PTQ = 180° - 80° = 100°
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