Q. 345.0( 1 Vote )

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
A. 105°

B. 135°

C. 140°

D. 145°

Answer :


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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