Question 73
In the exterior of the acute-angled triangle $ABC$, we construct the isosceles triangles $DAB$ and $EAC$ with bases $AB$ and $AC$, respectively, such that $\angle DBC = \angle ECB = 90^\circ$. Let $M$ and $N$ be the reflections of $A$ with respect to $D$ and $E$, respectively. Prove that the line $MN$ passes through the orthocenter of the triangle $ABC$.