VMO 1991 Problem 3
The lines L, M, N in space are mutually perpendicular. A variable sphere passes through three fixed points A on L, B on M, C on N and meets the lines again at A', B', C'. Find the locus of the midpoint of the line joining the centroids of ABC and A'B'C'.
Community text Kalva (prase.cz mirror). Quoted with source.
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