IMO 1971 LL POL38

Let A, B, C be three points with integer coordinates in the

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IMO 1971 LL POL38

Origin: POL

Problem

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\cdotBC\cdotCA \geq2R, and if the center of K is in the origin of the coordinates, show that AB \cdot BC \cdot CA \geq4R.