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MMO 329 Moscow MO 1956 point on altitude of tetrahedron, given areas

Source:

August 19, 2019
geometry3D geometrytetrahedronLocusaltitudearea

Problem Statement

Consider positive numbers h,s1,s2h, s_1, s_2, and a spatial triangle △ABC\vartriangle ABC. How many ways are there to select a point DD so that the height of tetrahedron ABCDABCD drawn from DD equals hh, and the areas of faces ACDACD and BCDBCD equal s1s_1 and s2s_2, respectively?
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