Question

iii.
In the adjoining figure, triangle ABC is an isosceles triangle with perimeter 44cm. The base BC is of length 12 cm. Sides AB and AC are congruent. A circle touches the three sides as shown. Find the length of a tangent segment from A to the circle.

Answer 1

The length of tangent segment = 16 cm

Step-by-step explanation:

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

Perimeter = 44 cm and base BC = 12 cm

Perimeter of triangle ABC = 44 cm

AB + BC + AC = 44 cm

AB + BC + AB = 44 cm..........[ side AB ≅ side AC]

2 AB + 12 = 44 ...........[ side AB = 12 cm]

2 AB = 32

  AB = 32/2

  AB = 16

Therefore, AB = AC = 16 cm

Then, The length of tangent segment from A to the circle = 16 cm