MathDB

Coplanar points on a sphere

Source: Germany 2010 - Problem 6

April 12, 2016

geometry3D geometrysphere

Problem Statement

Let

A,B,C,D,E,F,G

and

H

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)

and

(D,A,E,H)

of points are coplanar. Prove that the quadruple

(E,F,G,H)

is coplanar aswell.