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Part of 1996 Czech And Slovak Olympiad IIIA

Problems(1)

exists a tetrahedron with max distance

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1996 p2

2/20/2020
Let AP,BQAP,BQ and CRCR be altitudes of an acute-angled triangle ABCABC. Show that for any point XX inside the triangle PQRPQR there exists a tetrahedron ABCDABCD such that XX is the point on the face ABCABC at the greatest distance from DD (measured along the surface of the tetrahedron).
geometry3D geometrytetrahedron