KöMaL 2009 B4209

In an acute triangle ABC , the feet of the altitudes drawn from $A$ and $B$ are $A_1$ and $B_1$, respectively, and the orthocentre of the triangle is $M$. The median drawn from $B$intersects line $A_1 B_1$ at point $P$. Prove that $BPM\sphericalangle$ is a right angle if and only if $B_1 C$=3$AB_1$.