Q. 105.0( 1 Vote )

If a chord AB subtends an angle of 60° at the center of a circle, then the angle between the tangents to the circle drawn from A and B is
A. 30°

B. 60°

C. 90°

D. 120°

Answer :


Let us consider a circle with center O and AB be a chord such that AOB = 60°


AP and BP are two intersecting tangents at point P at point A and B respectively on the circle.


To find : Angle between tangents, i.e. APB


As AP and BP are tangents to given circle,


We have,


OA AP and OB BP [Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


So, OAP = OBP = 90°


In quadrilateral AOBP, By angle sum property of quadrilateral, we have


OAP + OBP + APB + AOB = 360°


90° + 90° + APB + 60° = 360°


APB = 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