Let $AA_1$ and $BB_1$ be the altitudes of acute angled triangle $ABC$. Points $K$ and $M$ are midpoints of $AB$ and $A_1B_1$ respectively. Segments $AA_1$ and $KM$ intersect at point $L$. Prove that points $A$, $K$, $L$ and $B_1$ are noncyclic. Proposed by S. Berlov
Problem
Source: St. Petersburg MO 2000, 10th grade, P2
Tags: geometry, altitudes, midpoints, cyclic quadrilateral