MathDB

6

Part of 2010 German National Olympiad

Problems(1)

Coplanar points on a sphere

Source: Germany 2010 - Problem 6

4/12/2016
Let A,B,C,D,E,F,GA,B,C,D,E,F,G and HH be eight pairwise distinct points on the surface of a sphere. The quadruples (A,B,C,D),(A,B,F,E),(B,C,G,F),(C,D,H,G)(A,B,C,D), (A,B,F,E),(B,C,G,F),(C,D,H,G) and (D,A,E,H)(D,A,E,H) of points are coplanar. Prove that the quadruple (E,F,G,H)(E,F,G,H) is coplanar aswell.
geometry3D geometrysphere