Question 76
In quadrilateral $ABCD$, $AC$ is the bisector of angle $A$ and $\angle ADC = \angle ACB$. $X$ and $Y$ are the feet of the altitudes from $A$ to $BC$ and $CD$, respectively. Prove that the orthocenter of triangle $AXY$ is located on line $BD$ (A triangle's orthocenter is the intersection point of its altitudes).