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find 2 points in plane so that t4 points form a regular tetrahedron

Source: Vietnam MO 1979 P6

July 28, 2018
geometry3-Dimensional Geometryconstructiontetrahedron3D geometry

Problem Statement

ABCDABCD is a rectangle with BC/AB=2BC / AB = \sqrt2. ABEFABEF is a congruent rectangle in a different plane. Find the angle DAFDAF such that the lines CACA and BFBF are perpendicular. In this configuration, find two points on the line CACA and two points on the line BFBF so that the four points form a regular tetrahedron.
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