Let the values of DH and CF be x and y respectively.
[ AE = AH = 4.5
BE = BF = 5.5
DH = DG = x
CF = CG = y ] [Tangent segment theorem] □ABCD is a parallelogram. [Given]
∴ AB = CD [Opposite sides of a parallelogram]
∴ AE + BE = DG + CG [A – E – B, D – G – C]
∴ 4.5 + 5.5 = x + y ∴ x + y = 10 ……….. (i)
Also, AD = BC [Opposite sides of a parallelogram]
∴ AH + DH = BF + CF [A – H – D, B – F – C]
∴ 4.5 + x = 5.5 + y
∴ x – y = 1 ………… (ii) Adding equations (i) and (ii), we get
2x = 11
∴ x = 11/2 = 5.5
∴ AD = AH + DH [A – H – D]
= 4.5 + 5.5
∴ AD = 10 units