to draw a pair of tangents to a circle which are inclined to each other at an angle of 100^{o }it is required to draw tangents at end points of those two radii of the circle, the angle between which should be??

Lalit Mehra , Meritnation Expert added an answer, on 21/2/12

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°.

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