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.

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

Chapter 3 – Circle – Text Book Solution

Problem Set 3 | Q 5 | Page 85

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.

In figure 3.85, c ABCD is a parallelogram
solution

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

Explanation:-

The given problem involves a parallelogram ABCD, where tangent segments are drawn from an external point to a circle. The aim is to find the value of AD, which is one of the sides of the parallelogram.

Given information:

Using equations (1), (2), and (7), we can write: 2AB = 2AD AB = AD

Therefore, we can conclude that AD is equal to AB, which is also equal to AE + EB. We are given that AE = 4.5 and EB = 5.5. Hence, AD = AB = AE + EB = 4.5 + 5.5 = 10 units.

Thus, the value of AD is 10 units.

Chapter 3 – Circle – Text Book Solution

Problem Set 3 | Q 5 | Page 84


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