Question 73
Let $ABC$ be a triangle inscribed in circle $(O)$ with $\angle A = 45^\circ$. Two rays $BO$, $CO$ intersect $AC$, $AB$ at $E$, $F$ respectively. The circumcircles of triangles $BOC$ and $EOF$ intersect at $K$. Let $J$ be circumcenter of triangle $AEF$. Prove that $JK$ passes through the orthocenter of triangle $ABC$.