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Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
In the given figure, if AB is a tangent to the circle with centre O such that OB = 6 cm and ∠AOB = 60°, then the length of OA is :
In the given figure, TP and TQ are tangents at points P and Q of the circle respectively. If reflex ∠ POQ = 250°, find the measure of each angle of quadrilateral POQT.
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°.
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.
Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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