In Fig. 2, a circle is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E, and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.

The figure can be redrawn as follows:

It is given in the question that,

AB = 12 cm

BC = 8 cm

AC = 10 cm

As we know that, tangents drawn from an external point in a triangle are equal

∴ AF = AD, CF = CE, BD = BE

Let us assume AD = AF = x cm

∴DB = AB – AD

= (12 – x) cm

Also, BE = (12 – x) cm

Similarly,

CF = CE = AC – AF

= (10 – x) cm

As, BC = 8 cm

∴ BE + CE = 8

12 – x + 10 – x = 8

22 – 8 = 2x

2x = 14

x = 7 cm

Hence, AD = x = 7 cm

BE = 12 – x

= 12 – 7

= 5 cm

And, CF = 10 – x

= 10 – 7

= 3 cm