Question 88
A circle is called *good colored* if the vertices of any equilateral triangle inscribed in this circle are colored in distinct colors. Let $k$ be a circle with radius $2$.
a) Is there a coloring of the points on $k$ and inside $k$ in three colors such that $k$ and any circle with radius at least $1$ that touches $k$ are good colored?
b) Is there such a coloring in seven colors?
a) Is there a coloring of the points on $k$ and inside $k$ in three colors such that $k$ and any circle with radius at least $1$ that touches $k$ are good colored?
b) Is there such a coloring in seven colors?