Team Selection Test for JBMO 2024

Let $ABC$ be an acute triangle, $P$ be the midpoint of the side $BC$ and $K$ be the foot of the altitude from $A$. Let $D$ be a point on the segment $AP$ such that $\angle BDC=90^{\circ }$. Let the second intersection point of the circumcircle of $ADK$ and line $BC$ be $E$. Let the second intersection point of the circumcircle of $ABC$ and line $AE$ be $F$. Prove that $\angle AFD=90^{\circ }$.