# In figure, if 0 is the center of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal toA. 100°B. 80°C. 90°D. 75°

Given : OP is a radius and PR is a tangent in a circle with center O with RPQ = 50°

To find : POQ

Now, OP PR [ As tangent to at any point on the circle is perpendicular to the radius through point of contact]

OPR = 90°

OPQ + RPQ = 90°

OPQ + 50° = 90°

OPQ = 40°

In POQ

OP = OQ [radii of same circle]

OQP = OPQ = 40° [ angles opposite to equal sides are equal] [1]

In OPQ By angle sum property of a triangle

OPQ + OPQ + POQ = 180°

40° + 40° + POQ = 180°

POQ = 100°

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Testing Your Knowledge on Circles32 mins
Quiz | Imp. Qs. on Circle35 mins
Important Questions on Circles46 mins
Smart Revision | Circles44 mins
Quiz | Imp. Qs. on Circles37 mins
RD Sharma | Important Questions on Circles36 mins
Short Cut Trick to Find Area of Triangle43 mins
Tangent from an External Point54 mins
RD Sharma | Most Important Questions of Circles35 mins
RD Sharma | Imp Qs Discussion on Area Related With Circles41 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