Each point of a plane is painted in one of three colors. Show that there exists a triangle such that:
(i) all three vertices of the triangle are of the same color;
(ii) the radius of the circumcircle of the triangle is 2008;
(iii) one angle of the triangle is either two or three times greater than one of the other two angles. geometrycircumcirclesearchcombinatorics proposedcombinatorics