FI-MO 2018 Problem 2

The sides of triangle $ABC$ are $a = | BC |, b = | CA |$ and $c = | AB |$ . Points $D, E$ and $F$ are the points on the sides $BC, CA$ and $AB$ such that $AD, BE$ and $CF$ are the angle bisectors of the triangle $ABC$ . Determine the lengths of the segments $AD, BE$ , and $CF$ in terms of $a, b$ , and $c$ .