If a chord AB subtends an angle of 60° at the center of a circle, then the angle between the tangents to the circle drawn from A and B is

Let us consider a circle with center O and AB be a chord 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 + 60° = 360°

APB = 120°