Question 91
Let $ABC$ be an acute triangle with $AB \neq AC$ and intersection point $H$. Let the center of the page $BC$ be $M$. Let the points $D$ on $AB$ and $E$ on $AC$ be such that $AE = AD$ and $D, H, E$ lie on a straight line. Show that $HM$ and the common chord of the circumcircles of the two triangles $ABC$ and $ADE$ are perpendicular to each other.