RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 14 of Exercise 12B

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

14

In the given figure, PA and PB are two tangents to the circle with center O. If APB = 60° then find the measure of OAB.

In the given figure, PA and PB are two tangents from common point P


PA = PB


[ Tangents drawn from an external point are equal]


PBA = PAB


[ Angles opposite to equal angles are equal] …[1]


By angle sum property of triangle in APB


APB + PBA + PAB = 180°


60° + PAB + PAB = 180° [From 1]


2PAB = 120°


PAB = 60° …[2]


Now,


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


OAB + PAB = 90°


OAB + 60° = 90° [From 2]


OAB = 30°


Chapter Exercises

More Exercise Questions