The sides AB, BC and AC of a $\triangle$ABC are 12 cm, 8 cm and 10 cm respectively. A circle is inscribed in the triangle touching AB, BC and AC at D, E and F, respectively. The difference between the lengths of AD and CE is:

3 cm 4 cm 5 cm 2 cm

4 cm

As we know, AD = AF, FC = CE and BE = BD [Tangents] Let AD = x and CE = y BD = 12 - x BE = 12 - x CE = BC - BE y = 8 - 12 + x y = x - 4 or x - y = 4 AD - CE = 4 cm