Question

In the given figure, ▢ABCD is a parallelogram. It circumscribes the circle with centre T. Point E, F, G, H are touching points. If AE = 4.5, EB = 5.5, find AD.

Answer 1

ABCD is a parallelogram.

∴ AB = CD       .....(1)       (Opposite sides of parallelogram are equal)

AD = BC          .....(2)       (Opposite sides of parallelogram are equal)

Tangent segments drawn from an external point to a circle are congruent.

AE = AH           .....(3)

DG = DH          .....(4)

BE = BF            .....(5)

CG = CF           .....(6)

Adding (3), (4), (5) and (6), we get

AE + BE + CG + DG = AH + DH + BF + CF

⇒ AB + CD = AD + BC      .....(7)

From (1), (2) and (7), we have

2AB = 2AD

⇒ AB = AD

∴ AD = AB = AE + EB = 4.5 + 5.5 = 10 units