In the given figure, a circle is inscribed in a quadrilateral ABCD which touches the sides AB, BC, CD and DA at P, Q, R and S respectively. Prove that ∠ AOB + ∠ COD = 180°.

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TextTheorem on Tangent Perpendicular to Radius at Point of ContactCBSE PYQ

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PA and PB are tangents to a circle with centre O. If ∠AOB = 105° then ∠OAP + ∠APB is equal to :

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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.

TextTheorem on Tangent Perpendicular to Radius at Point of Contact