Q. 145.0( 2 Votes )

In the given figure, O is the center of a circle, PQ is a chord and PT is the tangent at P. If POQ = 70°, then TPQ is equal to


A. 35°

B. 45°

C. 55°

D. 70°

Answer :

In OPQ


POQ = 70° [Given]


OP = OQ [radii of same circle]


OQP = OPQ [Angles opposite to equal sides are equal]


By angle sum Property of triangle,


POQ + OQP + OPQ = 180°


70° + OPQ + OPQ = 180°


2 OPQ = 110°


OPQ = 55°


Now,


OPT = 90°


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


OPQ + TPQ = 90°


55° + TPQ = 90°


TPQ = 35°

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