RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 20 of Multiple Choice Questions (MCQ)

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20

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

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…[1]


[Angles opposite to equal angles are equal]


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°

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