Estonian Math Competitions 2006/2007
Source: Seniors Problem 8
July 29, 2008
geometrycircumcircleinradiustrigonometrygeometry unsolved
Problem Statement
Consider triangles whose each side length squared is a rational number. Is it true
that
(a) the square of the circumradius of every such triangle is rational;
(b) the square of the inradius of every such triangle is rational?