Question 107
$D$ is the midpoint of the side $BC$ of the given triangle $ABC$. $M$ is a point on the side $BC$ such that $\angle BAM = \angle DAC$. $L$ is the second intersection point of the circumcircle of the triangle $CAM$ with the side $AB$. $K$ is the second intersection point of the circumcircle of the triangle $BAM$ with the side $AC$. Prove that $KL \parallel BC$.