Q. 85.0( 1 Vote )

PQ is a tangent to a circle with center O at the point P. If ΔOPQ is an isosceles triangle, then OQP is equal to
A. 30°

B. 45°

C. 60°

D. 90°

Answer :


Let us consider a circle with center O and PQ is a tangent


on the circle, Joined OP and OQ


But OPQ is an isosceles triangle, OP = PQ


OQP = POQ


[Angles opposite to equal sides are equal]


In OQP


OQP + OPQ + POQ = 180°


[Angle sum property of triangle]


OQP + 90° + OPQ = 180°


2 OPQ = 90°


OPQ = 45°

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