Nice concurrence and collinearity
Source: VII Centroamerican and Caribbean Olympiad 2005, Problem 3
July 29, 2005
geometrycircumcircleincentergeometric transformationhomothetyEulergeometry proposed
Problem Statement
Let be a triangle. , and are the points of contact of the incircle with sides , and , respectively. Let , and be the feet of the altitudes of the triangle from , and , respectively.
a) Show that the lines , and meet at a point.
b) Prove that this points belongs to the line joining the orthocenter and the circumcenter of triangle .
Aarón Ramírez, El Salvador