Question

if a pair of tangents to a circle which are inclined to each other at an angle of 60° then find the degree measure of angle poq

Answer 1

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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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