RU-ALLRUSSIAN 2009 Problem 113

Let $ABCD$ be a triangular pyramid such that no face of the pyramid is a right triangle and the orthocenters of triangles $ABC$ , $ABD$ , and $ACD$ are collinear. Prove that the center of the sphere circumscribed to the pyramid lies on the plane passing through the midpoints of $AB$ , $AC$ and $AD$ .