Rational triangles
Source: Tournament of towns, Junior A-Level paper, Fall 2004
December 25, 2004
geometrygeometric transformationreflectionincentercircumcirclegeometry unsolved
Problem Statement
Let us call a triangle rational if each of its angles is a rational number when measured in degrees. Let us call a point inside triangle rational if joining it to the three vertices of the triangle we get three rational triangles. Show that any acute rational triangle contains at least three distinct rational points.