ILL 1971 Problem 38

Let $A,B,C$ be three points with integer coordinates in the plane and $K$ a circle with radius $R$ passing through $A,B,C$ . Show that $AB\cdot BC\cdot CA\ge 2R$ , and if the centre of $K$ is in the origin of the coordinates, show that $AB\cdot BC\cdot CA\ge 4R$ .