Question 129
In a tetrahedron $ABCD$, none of the face angles is $90^\circ$, and the orthocenters of the faces $ABC$, $ABD$, $ACD$ are collinear. Prove that the circumcenter of this tetrahedron is coplanar with the midpoints of edges $AB$, $AC$ and $AD$. (I. Bogdanov)