KöMaL 2012 B4494

$F$ is the midpoint of base $BC$ of the isosceles triangle ABC . $D$ is an interior point of the line segment $BF$. The perpendicular dropped from point $D$onto $BC$ intersects side $AB$ at $M$, and the line through point $D$, parallel to $AB$ intersects side $AC$ at $P$. Express the ratio of the areas of triangles AMP and ABC in terms of $k$=$BD$:$BC$.