In the figure, a circle touches all the four sides of a quadrilateral ABCD whose sides AB = 6.5 cm, BC = 5.4 cm and CD = 5.3 cm. The length of AD is:

Given, AB = 6.5 cm, BC = 5.4 cm and CD = 5.3 cm

Let the circle touches AB, BC, CD, DA at T, R, Q, S respectively.

Length of tangents to the circle from an external point are equal.

AT = AS

BT = BR

CQ = CR

DQ = DS

Adding all of the above

AT + BT + CQ + DQ = AS + BR + CR + DS

$$\Rightarrow$$  (AT + BT) + (CQ + DQ) = (AS + DS) + (BR + CR)

$$\Rightarrow$$  AB + CD = AD + BC

$$\Rightarrow$$  6.5 + 5.3 = AD + 5.4

$$\Rightarrow$$  AD = 6.4 cm

Hence, the correct answer is Option D