CAPS 2001 Problem 2

A triangle $ABC$ has acute angles at $A$ and $B$ . Isosceles triangles $ACD$ and $BCE$ with bases $AC$ and $BC$ are constructed externally to triangle $ABC$ such that $\angle ADC = \angle ABC$ and $\angle BEC = \angle BAC$ . Let $S$ be the circumcenter of $\triangle ABC$ . Prove that the length of the polygonal line $DSE$ equals the perimeter of triangle $ABC$ if and only if $\angle ACB$ is right.