# Altitudes and Circumcircle

I'm given the following problem and hint, but I solved the problem another way. I was wondering whether my proof is correct; namely, am I making any wrong assumptions? Thank you.

Altitude $AD$ of $\triangle ABC$ has been extended to meet the circumcircle at point $X$. Point $H$ was chosen on line $AD$ so that $HD=DX$. Show that $BH$ is perpendicular to $AC$. HINT: Let $P$ be the point where $BH$ crosses the circle and show that arc $PAC$ is equal in measure to arc $XC$.


... whose reflection on line BC lie on the circumcenter of $\triangle ABC$.
... whose reflection on line BC lie on the $\color{red}{\text{circumcircle}}$ of $\triangle ABC$.