Equal circles with centres O and O’ touch each other at X. OO’ produced to meet a circle with centre O’, at A. AC is tangent to the circle whose centre is O. O’ D is perpendicular to AC. Find the value of .

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.

In Fig. 10.65, common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

In Fig. 10.67, OQ:PQ=3:4 and perimeter of = 60 cm. Determine PQ, OR and OP.

Two concentric circles are of diameters 30 cm and 18 cm. Find the length of the chord of the larger circle which touches the smaller circle.