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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,
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°