Q. 24.8( 8 Votes )

If the angle between two radii of a circle is 130° then the angle between the tangents at the ends of the radii is
A. 65°

B. 40°

C. 50°

D. 90°

Answer :


Let us consider a circle with center O and OA and OB are two radii 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 + 130° = 360°


APB = 50°

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