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Question

The angle between two tangents drawn from an external point to a circle is _______ to the angle subtended by the line segments joining the points of contact at the centre.

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Solution




PA and PB are two tangents drawn from P to circle with centre O.

Now,

∠OAP = 90º (Radius is perpendicular to the tangent at the point of contact)

Also, ∠OBP = 90º (Radius is perpendicular to the tangent at the point of contact)

In quadrilateral OAPB,

∠AOB + ∠OAP + ∠OBP + ∠APB = 360º (Angle sum property of quadrilateral)

⇒ ∠AOB + 90º + 90º + ∠APB = 360º

⇒ ∠AOB + ∠APB = 360º − 180º = 180º

Thus, the angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.


The angle between two tangents drawn from an external point to a circle is __supplementary__ to the angle subtended by the line segments joining the points of contact at the centre.

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