Q. 134.2( 21 Votes )

In the given figure, PQ is a chord of a circle with center 0 and PT is a tangent. If QPT = 60°, find P


Answer :

Given : , PQ is a chord of a circle with center 0 and PT is a tangent and QPT = 60°.


To Find : PRQ


OPT = 90°


OPQ + QPT = 90°


OPQ + 60° = 90°


OPQ = 30° … [1]


Also.


OP = OQ [radii of same circle]


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


From [1], OQP = OQP = 30°


In OPQ , By angle sum property


OQP + OPQ + POQ = 180°


30° + 30° + POQ = 180°


POQ = 120°


As we know, the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.


So, we have


2PRQ = reflex POQ


2PRQ = 360° - POQ


2PRQ = 360° - 120° = 240°


PRQ = 120°


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 CircleQuiz | Imp. Qs. on CircleQuiz | Imp. Qs. on Circle35 mins
Quiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of Triangle43 mins
Quiz | Areas Related to CirclesQuiz | Areas Related to CirclesQuiz | Areas Related to Circles43 mins
RD Sharma |  Area of Sector and SegmentsRD Sharma |  Area of Sector and SegmentsRD Sharma | Area of Sector and Segments25 mins
Quiz | Area Related with CirclesQuiz | Area Related with CirclesQuiz | 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
caricature
view all courses