Faithful Lines - [Iran Second Round 1989]
Source:
December 6, 2010
geometrygeometric transformationreflectiongeometry proposed
Problem Statement
A line is called faithful to triangle if be in plane of triangle and the reflections of over the sides of be concurrent. Prove that for any two triangles with acute angles lying in the same plane, either there exists exactly one faithful line to both of them, or there exist infinitely faithful lines to them.