In figure 3.85, ABCD is a parallelogram. It circumscribes the circle with centre T.

Given ABCD is a parallelogram.
AB = DC ……(i) [Opposite sides of parallelogram are equal]
AD = BC ………(ii)
AE = AH………(iii) [Two tangents from a common point are congruent]
BE = BF……….(iv)
CG = CF………..(v)
DG = DH………..(vi)
Adding (iii), (iv), (v),(vi)
AE+BE+CG+DG = AH+BF+CF+DH
AB+CD = AD+BC ……(vii) [AH+DH = AD, BF+CF = BC]
From (i), (ii) and (vii)
2AB = 2AD
AB = AD
AD = AB = AE +EB = 4.5+5.5 = 10
Hence measure of AD is 10 units.