A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:

13

CR = CQ = 5 cm

BQ = BC - CQ

= 12 - 5 = 7 cm

BQ = BP = 7 cm   ...(1)

AS = AP = 6 cm   ..(2)

Adding equation (1) and (2), we get

= 7 + 6

= 13 cm

Therefore, length of AB is 13 cm.