tetrahedron
Source: All-Russian olympiad 1995, Grade 11, Second Day, Problem 7
October 20, 2013
geometry3D geometrytetrahedronratiogeometry proposed
Problem Statement
The altitudes of a tetrahedron intersect in a point. Prove that this point, the foot of one of the altitudes, and the points dividing the other three altitudes in the ratio (measuring from the vertices) lie on a sphere.
D. Tereshin