Question

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, Bc = 8 cm and AC = 10 cm, find the lengths fo AD, BE and CF.

Answer 1

Let AD = x, so, BD = 12 - z

BE =x, so, EC = 8-x

CF = y, so Af = 10 -y

BD = BE

CE = CF

AD = AF

ie, 12-z = x

= x + z = 12 .. . . . . . .. . . 1

8-x = y

=y+x = 8 . .. . . . . . .. . . . 2

10-y = z

z + y = 10 .. . . .. . . . . . . .3

Adding x, y and z

x + y + z = 12 -z + 8- x +10 -y

= 2( x+ y + z) = 30

x + y + z = 15 . . .. . . . .. . . .4

Now subtract 1 from 4

x + y+ z - ( x + z) = 15-12

y = CF = 3

Subtract 2 from 4

x + +y +z - (y+x) = 15-8

z = AD = 7

Subtract 3 from 4

x + y+ z -(z +y) = 15 - 10

x = BE = 5

Therfore, AD = 7, BE = 5 and CF = 3