to draw a pair of tangents to a circle which are inclined to each other at an angle of 100o it is required to draw tangents at end points of those two radii of the circle, the angle between which should be??
PA and PB are tangents drawn from an external point P to the circle.
∠OAP = ∠OBP = 90° (Radius is perpendicular to the tangent at point of contact)
In quadrilateral OAPB,
∠APB + ∠OAD + ∠AOD + ∠OBP = 360°
∴ 100° + 90° + ∠AOB + 90° = 360°
⇒ 280° + ∠AOB = 360°
⇒ ∠AOB = 360° – 280° = 80°
Thus, the angle between the two radius, OA and OB is 80°.