MathDB
diameter of circumcircle <= product of sides, lattice points

Source: Polish MO Second Round 1972 p3

September 8, 2024
geometrycircumcircleanalytic geometrylattice pointsgeometric inequality

Problem Statement

The coordinates of the triangle's vertices in the Cartesian system XOYXOY are integers. Prove that the diameter of the circle circumscribed by this triangle is not greater than the product of the lengths of the triangle's sides.