OPM 2012 Problem 2

In triangle $[ABC]$ , the bissector of the angle $\angle{BAC}$ intersects the side $[BC]$ at $D$ . Suppose that $\overline{AD}=\overline{CD}$ . Find the lengths $\overline{BC}$ , $\overline{AC}$ and $\overline{AB}$ that minimize the perimeter of $[ABC]$ , given that all the sides of the triangles $[ABC]$ and $[ADC]$ have integer lengths.