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ratio DD'/AB wanted, ABCD, ABCD' congruent tetrahedra

Source: 1964 Hungary - Kürschák Competition p1

October 11, 2022
ratiogeometrytetrahedron3D geometry

Problem Statement

ABCABC is an equilateral triangle. DD andD′ D' are points on opposite sides of the plane ABCABC such that the two tetrahedra ABCDABCD and ABCD′ABCD' are congruent (but not necessarily with the vertices in that order). If the polyhedron with the five vertices A,B,C,D,D′A, B, C, D, D' is such that the angle between any two adjacent faces is the same, find DD′/ABDD'/AB .
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