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IMO LongList 1967, Italy 2

Source: IMO LongList 1967, Italy 2

December 16, 2004
geometry3D geometrytetrahedronperpendicular bisectorIMO ShortlistIMO Longlist

Problem Statement

Let ABCDABCD be a regular tetrahedron. To an arbitrary point MM on one edge, say CDCD, corresponds the point P=P(M)P = P(M) which is the intersection of two lines AHAH and BKBK, drawn from AA orthogonally to BMBM and from BB orthogonally to AMAM. What is the locus of PP when MM varies ?
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