Let $AA_1$ and $CC_1$ be altitudes of acute angled triangle $ABC$. A point $D$ is chosen on $AA_1$ such that $A_1D=C_1D$. Let $E$ be the midpoint of $AC$. Prove that points $A$, $C_1$, $D$, $E$ are concylic. Proposed by S. Berlov
Problem
Source: St. Petersburg MO 2000, 9th grade, P2
Tags: geometry, Angle Chasing, St. Petersburg MO