Question

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°.

PQ and PR are tangents to the circle of radius 3 cm and centre O. If length of each tangent is 4 cm, then perimeter of △ OQP is :

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

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.