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:

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