Question 122
Let $M$, $N$ and $P$ be the midpoints of the sides $BC$, $AC$ and $AB$ in triangle $ABC$, respectively. Suppose that the point $K$ lies on the segment $NP$ such that $AK$ is the angle bisector of $\angle BKC$. The lines $BK$ and $MN$ meet at a point $E$ and the lines $CK$ and $MP$ meet at a point $F$. Let $H$ be the foot of the altitude from $A$ to $BC$, and let the circumcircle of triangle $AKH$ intersect the circumcircle of triangle $EFH$ for the second time at $L$. Prove that lines $EF$, $MK$ and $HL$ are concurrent.