RO-TST 2012 Problem 2

Let $ABCD$ be a cyclic quadrilateral such that the triangles $BCD$ and $CDA$ are not equilateral. Prove that if the Simson line of $A$ with respect to $\triangle BCD$ is perpendicular to the Euler line of $BCD$ , then the Simson line of $B$ with respect to $\triangle ACD$ is perpendicular to the Euler line of $\triangle ACD$ .