Explanation:

Let’s break it down:

- In a tangential quadrilateral (where a circle touches all sides), the tangents from a single point to the circle are equal.

- So, from A, the segments to S and P have the same length: AS = AP = 6 cm.

- Similarly, from C, the segments to R and Q are the same: CR = CQ = 5 cm.

- The lengths of the sides are:

- AB: AP + PB

- BC: BQ + QC

- CD: CR + RD

- DA: DS + SA

- Let’s assign:

- AP = AS = 6

- BQ = BP (from B)

- CR = CQ = 5

- DS = DR (from D)

- The full side BC is BQ + QC = BQ + 5 = 12, so BQ = 7 cm.

- AB = AP + PB = 6 + PB. But PB = BQ = 7.

- So, AB = 6 + 7 = 13 cm

- Options:

- 13

- 11

- 15

- 12

- So, option 1 is correct. Your answer matches.