ILL 1984 Problem 26
A cylindrical container has height and radius . It rests on a circular hoop, also of radius , fixed in a horizontal plane with its axis vertical and with each circular rim of the cylinder touching the hoop at two points. The cylinder is now moved so that each of its circular rims still touches the hoop in two points. Find with proof the locus of one of the cylinder's vertical ends.
Dataset text AI-MO AoPS. Quoted with source.
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