NL-BXMO-TST 2020 Problem 2

In an acute-angled triangle $ABC, D$ is the foot of the altitude from $A$ . Let $D_1$ and $D_2$ be the symmetric points of $D$ wrt $AB$ and $AC$ , respectively. Let $E_1$ be the intersection of $BC$ and the line through $D_1$ parallel to $AB$ . Let $E_2$ be the intersection of $BC$ and the line through $D_2$ parallel to $AC$ . Prove that $D_1, D_2, E_1$ and $E_2$ on one circle whose center lies on the circumscribed circle of $\vartriangle ABC$ .