Colors of point
Source: Yugoslavia National Olympiad 2008
April 22, 2008
geometrycircumcirclesearchcombinatorics proposedcombinatorics
Problem Statement
Each point of a plane is painted in one of three colors. Show that there exists a triangle such that:
all three vertices of the triangle are of the same color;
the radius of the circumcircle of the triangle is ;
one angle of the triangle is either two or three times greater than one of the other two angles.