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collinearity with a sphere

Source: Polish MO second round 1959 p6

August 29, 2024
geometrycollinearsphere3D geometry

Problem Statement

From a point M M on the surface of a sphere, three mutually perpendicular chords MA MA , MB MB , MC MC are drawn. Prove that the segment joining the point M M with the center of the sphere intersects the plane of the triangle ABC ABC at the center of gravity of this triangle.
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