MathDB
2017 IGO Advanced P5

Source: 4th Iranian Geometry Olympiad (Advanced) P5

September 15, 2017
IGOIrangeometry3D geometryspheretetrahedron

Problem Statement

Sphere SS touches a plane. Let A,B,C,DA,B,C,D be four points on the plane such that no three of them are collinear. Consider the point A′A' such that SS in tangent to the faces of tetrahedron A′BCDA'BCD. Points B′,C′,D′B',C',D' are defined similarly. Prove that A′,B′,C′,D′A',B',C',D' are coplanar and the plane A′B′C′D′A'B'C'D' touches SS.
Proposed by Alexey Zaslavsky (Russia)
Back to ProblemsView on AoPS