Coloring the plane with two colors
Suppose that each point of the plane is painted either red or green.
Then there always exist
A) two points with distance 2019, such that the two points are painted with the same color,
B) a rectangle, such that its vertices are painted with the same color,
C) a triangle, such that its vertices and centroid are painted with the same color,
D) a triangle, such that its vertices and incenter are painted with the same color.
How many of the statements above is (always) true?
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