Q. 195.0( 1 Vote )

In the given figure, 0 is the center of a circle and PT is the tangent to the circle. If PQ is a chord such that QPT = 50° then POQ = ?


A. 100°

B. 90°

C. 80°

D. 75°

Answer :

In the given figure PT is a tangent to circle we have


OPT = 90°


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


OPQ + QPT = 90°


OPQ + 50° = 90°


OPQ = 40°


Now, In POQ


OP = OQ


PQO = QPO = 40°


[Angles opposite to equal sides are equal]


Now,


PQO + QPO + POQ = 180°


[By angle sum property of triangle]


40° + 40° + POQ = 180°


POQ = 100°

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