MathNet 2010 — Part 06 Question 141

The diagonals of a cyclic quadrilateral $ABCD$ are perpendicular. Points $K, L, M, Q$ are the orthocenters of the triangles $ABD$, $ACD$, $BCD$, $ABC$ respectively. Prove that quadrilaterals $KLMQ$ and $ABCD$ are equal.