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

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,


[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°