Question 64
Let $ABC$ be a triangle with circumcenter $O$. Point $X$ is the intersection of the parallel line from $O$ to $AB$ with the perpendicular line to $AC$ from $C$. Let $Y$ be the point where the external bisector of $\angle BXC$ intersects with $AC$. Let $K$ be the projection of $X$ onto $BY$.
Prove that the lines $AK$, $XO$, $BC$ have a common point.
Prove that the lines $AK$, $XO$, $BC$ have a common point.