MathDB
Cono Sur Olympiad 2005, Problem 2

Source:

August 19, 2014
geometrycircumcircletrigonometrygeometry proposed

Problem Statement

Let ABCABC be an acute-angled triangle and let ANAN, BMBM and CPCP the altitudes with respect to the sides BCBC, CACA and ABAB, respectively. Let RR, SS be the pojections of NN on the sides ABAB, CACA, respectively, and let QQ, WW be the projections of NN on the altitudes BMBM and CPCP, respectively.
(a) Show that RR, QQ, WW, SS are collinear. (b) Show that MP=RSāˆ’QWMP=RS-QW.