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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,
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°