In figure (i) given below, quadrilateral ABCD is circumscribed ; find the perimeter of quadrilateral ABCD.

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

∴ AS = AP = 6 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

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

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

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

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

From D, DS and DR are the tangents to the circle.

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

Therefore, perimeter of the quadrilateral ABCD

$= AB + BC + CD + DA \\[1em] = AP + BP + BQ + CQ + CR + DR + DS + AS \\[1em] = 6 + 5 + 5 + 3 + 3 + 4 + 4 + 6 \\[1em] = 36 \text{ cm}$

Hence, the perimeter of ABCD = 36 cm.