MathDB
Pyramid

Source: APMC 2006, Problem 10

September 9, 2006
geometry3D geometrypyramidgeometry proposed

Problem Statement

Let ABCDSABCDS be a (not neccessarily straight) pyramid with a rectangular base ABCDABCD and acute triangular faces ABS,BCS,CDS,DASABS,BCS,CDS,DAS. We consider all cuboids which are inscribed inside the pyramid with its base being in the plane ABCDABCD and its upper vertexes are in the triangular faces (one in each). Find the locus of the midpoints of these cuboids.
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