Q. 35.0( 2 Votes )

If tangents PA and PB from a point P to a circle with center O are drawn so that APB = 80° then POA = ?


A. 40°

B. 50°

C. 80°

D. 60°

Answer :

In AOP and BOP


AP = BP


[Tangents drawn from an external point are equal]


OP = OP [Common]


OA = OB


[Radii of same circle]


AOP BOP


[By Side - Side - Side criterion]


APO = BPO


[Corresponding parts of congruent triangles are congruent]


APB = APO + BPO


80 = APO + APO


2APO = 80


APO = 40°


In AOP


APO + AOP + OAP = 180°


[By angle sum property]


40° + AOP + 90° = 180°


[ OAP = 90° as OA AP because Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


AOP = 50°

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