MathDB
Bulgaria 1999 Geometric NT

Source:

November 14, 2012
analytic geometryratiogeometrycircumcircleinradiusnumber theory

Problem Statement

The vertices of a triangle have integer coordinates and one of its sides is of length n\sqrt{n}, where nn is a square-free natural number. Prove that the ratio of the circumradius and the inradius is an irrational number.