In Fig. 10.63, two tangents AB and AC are drawn to a circle with centre O such that . Prove that OA = 2AB.

In Fig. 10.61, BDC is a tangent to the given circle at point D such that BD = 30 cm and CD = 7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF (ii) radius of the circle.

In Fig. 10.62, . The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisectors of each other.

In Fig. 10.64, BC is a tangent to the circle O. OE bisects AP. Prove that .

The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm and 7 cm respectively. Determine the length of the fourth side.