Q. 18 B3.7( 3 Votes )

Centre of the circle is O and AP, and AQ is tangent of the circle. If OPQ=20°, then what is the value of PAQ?

Answer :


OPQ = 20° …given


Radius OP is perpendicular to tangent PA at point of contact A


APO = 90°


From figure APO = APQ + OPQ


90° = APQ + 20°


APQ = 70° …(a)


Consider ΔAPQ


AP and AQ are tangents to circle from A


Tangents from a point to a circle are equal


AP = AQ
hence ΔAPQ is a isosceles triangle


APQ = AQP


Using (a)


AQP = 70°


Now


APQ + AQP + PAQ = 180° …sum of angles of triangle


70° + 70° + PAQ = 180°


140° + PAQ = 180°


PAQ = 40°


Hence PAQ is 40°



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