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°

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