Question

A circle is inscribed in a ABC, with sides AC, AB and BC as 8 cm, 10 cm and 12 cm

respectively (see below figure). Find the length of BE and CF.​

Answer 1

Hi✌️✌️

Solution:

We know that tangents from an external point are equal in length.

Given :

AB = 12 cm

BC= 8 cm

AC = 10 cm

Now let us take A as external point,thus

AD = AF

let AD = AF = x cm

So, DB = 12-x = BE [tangent from external point B]

CE = 8-12+x = -4+x = CF [tangent from external point C]

Since perimeter of ∆ABC does not change so

12+8+10= x+x+12-x+12-x-4+x-4+x

30=2x+16

2x=30-16

2x=14

x = 7 cm

So, AD = AE = 7 cm

BD=BE = 12-7=5 cm

CE=CF= -4+7=3 cm

Hope it helps you.