Question 29
We are given an acute triangle $ABC$ with $AB \gt AC$ and orthocenter $H$. The point $E$ lies symmetric to $C$ with respect to the altitude $AH$. Let $F$ be the intersection of the lines $EH$ and $AC$.
Prove that the circumcenter of the triangle $AEF$ lies on the line $AB$.
Prove that the circumcenter of the triangle $AEF$ lies on the line $AB$.