Question 104
In an acute triangle $ABC$ the foot of the altitude from $A$ is called $D$. Let $D_1$ and $D_2$ be reflections of $D$ in $AB$ and $AC$, respectively. The intersection of $BC$ and the line through $D_1$ parallel to $AB$, is called $E_1$. The intersection of $BC$ and the line through $D_2$ parallel to $AC$, is called $E_2$. Prove that $D_1, D_2, E_1$, and $E_2$ lie on a circle whose centre lies on the circumcircle of $\triangle ABC$.