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 toA. 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°

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Imp. Qs. on Circle35 mins
Quiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of Triangle43 mins
Quiz | Areas Related to Circles43 mins
RD Sharma | Area of Sector and Segments25 mins
Quiz | Area Related with Circles47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses