#### Question

In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.

#### Solution

Given:- In an isosceles triangle ΔABC side AB ≅ side AC,

Perimeter = 44 cm and base BC = 12 cm.

Perimeter of ΔABC = 44 cm

AB + BC + AC = 44

AB + BC + AB = 44 .............(side AB ≅ side AC)

2AB + 12 = 44 ..............(side BC = 12)

2AB = 44 - 12 = 32

AB = 32/2 = 16

AB = AC = 16

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#### APPEARS IN

Solution In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle. Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle.