In Fig. 10.69, AB is a diameter of a circle with centre O and AT is a tangent. If , find .

A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of is 336 cm², find the sides PQ and PR.

In Fig. 10.68, a is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of is 84 cm².

In Fig. 10.70, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30^o. A chord RS is drawn parallel to the tangent PQ. Find  ∠RQS.

In Fig. 10.72, PA and PB are tangents to the circle drawn from an external point P. CD are a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?