Problem #PRU-65555

Problems Calculus Real numbers Rational and irrational numbers Geometry Plane geometry Triangles Remarkable points and lines in a triangle

Problem

Author: A.V. Shapovalov

We call a triangle rational if all of its angles are measured by a rational number of degrees. We call a point inside the triangle rational if, when we join it by segments with vertices, we get three rational triangles. Prove that within any acute-angled rational triangle there are at least three distinct rational points.