In figure (ii) given below, quadrilateral ABCD is circumscribed, find x.

From A, AP and AQ are the tangents to the circle.

∴ AP = AQ = 5 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From C, CR and CS are the tangents to the circle.

∴ CS = CR = 3 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From figure,

BS = BC - CS = 7 - 3 = 4 cm.

From B, BS and BP are the tangents to the circle.

∴ BP = BS = 4 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From figure,

x = BP + AP = 4 + 5 = 9 cm.

Hence, the value of x = 9 cm.