MathDB
another solid geometry problem

Source: RMO District 2005, 10th Grade, Problem 3

March 5, 2005
geometry3D geometrytetrahedroncircumcirclegeometry proposed

Problem Statement

Let OO be a point equally distanced from the vertices of the tetrahedron ABCDABCD. If the distances from OO to the planes (BCD)(BCD), (ACD)(ACD), (ABD)(ABD) and (ABC)(ABC) are equal, prove that the sum of the distances from a point Māˆˆint[ABCD]M \in \textrm{int}[ABCD], to the four planes, is constant.
Back to ProblemsView on AoPS