Question 23
Let $ABC$ be an acute triangle and let $P$ be the intersection of the tangents in $B$ and $C$ to the circumcircle of $\triangle ABC$. The line through $A$ perpendicular to $AB$ and the line through $C$ perpendicular to $AC$ intersect in a point $X$. The line through $A$ perpendicular to $AC$ and the line through $B$ perpendicular to $AB$ intersect in a point $Y$. Prove that $AP \perp XY$.