Question 48
Let $ABC$ be a triangle inscribed in circle $(O)$ with angle $\angle A = 45^\circ$ and $AB \lt AC$. Let $AD, AH$ be the angle bisector and altitude of triangle $ABC$ with $D, H$ are on $BC$. Suppose that $OD$ intersects $AH$ at $E$ and $K$ is the circumcenter of triangle $EBC$. Prove that $HK \parallel AD$.