Question 3
(BEL 3) IMO4. We say that a set $E$ of points of the Euclidian plane is “Pythagorean” if for any partition of $E$ into two sets $A$ and $B$, at least one of the sets contains the vertices of a right-angled triangle. Decide whether the following sets are Pythagorean:
(a) a circle;
(b) an equilateral triangle (that is, the set of three vertices and the points of the three edges).
(a) a circle;
(b) an equilateral triangle (that is, the set of three vertices and the points of the three edges).