1983 IMO 第 3 题

(BEL 3) $)^{\mathrm{IMO} 4}$ 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).

(BEL 3) $)^{\mathrm{IMO} 4}$ 如果将 $E$ 任意划分为两个集合 $A$ 和 $B$，至少其中一个集合包含直角三角形的顶点，则我们说欧几里德平面上的点集合 $E$ 是“毕达哥拉斯”的。判断下列集合是否是毕达哥拉斯集合： (a) 圆； (b) 等边三角形(即三个顶点和三个边的点的集合)。