Question 145
In acute triangle $ABC$, let $D$ be the foot of the altitude from $A$. Reflect $D$ across $AB$ and $AC$ to obtain $D_1$ and $D_2$. The line through $D_1$ parallel to $AB$ meets $BC$ at $E_1$, and the line through $D_2$ parallel to $AC$ meets $BC$ at $E_2$. Prove that $D_1,D_2,E_1,E_2$ lie on a circle whose center lies on the circumcircle of $ABC$.
