IMO Shortlist 1962 problem 3
Consider the cube ( and are the upper and lower bases, repsectively, and edges are parallel). The point moves at a constant speed along the perimeter of the square in the direction , and the point moves at the same rate along the perimiter of the square in the direction . Points and begin their motion at the same instant from the starting positions and , respectively. Determine and draw the locus of the midpionts of the segments .