PE-MO 2018

Let $ABC$ be an acute triangle such that $BA = BC$ . On the sides $BA$ and $BC$ points $D$ and $E$ are chosen respectively, such that $DE$ and $AC$ are parallel. Let $H$ be the orthocenter of the triangle $DBE$ and $M$ be the midpoint of $AE$ . If $\angle HMC = 90^o$ , determine the measure of angle $\angle ABC$ .