$HOMF$ is a rectangle in which $HO = 11$, $OM = 5$. The orthocenter of $\triangle ABC$ is $H$, circumcenter $O$, midpoint of $BC$ is $M, F$ is the endpoint of the normal drawn from vertex $A$ to $BC$($F$ is on $BC$). Find the Value of $BC$.

Orthocenter: The point that intersects the three normals drawn from each vertex to the opposite side of a triangle.

Circumcenter: The center of the circle touching all the vertices of a triangle

Source: Putnam