Cono Sur Olympiad 2005, Problem 2
Source:
August 19, 2014
geometrycircumcircletrigonometrygeometry proposed
Problem Statement
Let be an acute-angled triangle and let , and the altitudes with respect to the sides , and , respectively. Let , be the pojections of on the sides , , respectively, and let , be the projections of on the altitudes and , respectively.(a) Show that , , , are collinear.
(b) Show that .