OBM 1999 Problem 6

Given any triangle $ABC$ , show how to construct $A'$ on the side $AB$ , $B'$ on the side $BC$ and $C'$ on the side $CA$ , such that $ABC$ and $A'B'C'$ are similar (with $\angle A = \angle A', \angle B = \angle B', \angle C = \angle C'$ ) and $A'B'C'$ has the least possible area.