IMO 1966 Problem 3
- Day 1
Prove that the sum of the distances of the vertices of a regular tetrahedron from the center of its circumscribed sphere is less than the sum of the distances of these vertices from any other point in space.
Official text Transcription from AI-MO AoPS, checked word for word against the official paper. Quoted with source.
Official text: IMO 1966 official English paper, page 1.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.