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  • Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

10.  Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

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To prove - \angle APB + \angle AOB = 180^0 
Proof-
We have, PA and PB are two tangents, B and A are the point of contacts of the tangent to a circle. And OA\perp PA , OB\perp PB (since tangents and radius are perpendiculars)

According to question,
In quadrilateral PAOB,
\angleOAP + \angleAPB +\anglePBO +\angleBOA = 360^0
90 + \angleAPB + 90 +\angleBOA = 360
\angle APB + \angle AOB = 180^0
Hence proved

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manish

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