RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 34 of Multiple Choice Questions (MCQ)

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34

To draw a pair of tangents to a circle, which is inclined to each other at an angle of 45°, we have to draw tangents at the end points of those two radii, the angle between which is


Let us consider a circle with center O and PA and PB are two tangents from point P, given that angle of inclination i.e. APB = 45°


As PA and PB are tangents to given circle,


We have,


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


So, OAP = OBP = 90°


In quadrilateral AQRP,


By angle sum property of quadrilateral, we have


OAP + OBP + ABP + AOB = 360°


90° + 90° + 45° + AOB = 360°


AOB = 135°

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