Q. 54.4( 5 Votes )

If PT is a tangent to a circle with center O and PQ is a chord of the circle such that QPT = 70°, then find the measure of POQ.


Answer :

Given: PT is a tangent to a circle with center O and PQ is a chord of the circle such that QPT = 70°


To Find: POQ = ?


Now,


OPT = 90°


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


OPQ + QPT = 90°


OPQ + 70° = 90°


OPQ = 20°


Also,


OP = OQ [Radii of same circle]


OQP = OPQ = 20°


[Angles opposite to equal sides are equal]


In OPQ By Angle sum property of triangles,


OPQ + OQP + POQ = 180°


20° + 20° + POQ = 180°


POQ = 140°


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