B. 4684. The diagonals of a quadrilateral \(\displaystyle ABCD\) are perpendicular, they intersect at \(\displaystyle E\). From point \(\displaystyle E\), drop a perpendicular onto the line of each side. Consider the intersection of each perpendicular with the opposite side. Prove that the four points all lie on a circle centred at a point of the line segment connecting the midpoints of the diagonals.
Suggested by Sz. Miklós, Herceghalom
Deadline expired on 10 February 2015.