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exists a tetrahedron with max distance

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

February 20, 2020
geometry3D geometrytetrahedron

Problem Statement

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).
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