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Problem 1 of RMO 2006 (Regional Mathematical Olympiad-India)

Source: Collinear Points

September 13, 2009
geometrygeometry unsolved

Problem Statement

Let ABC ABC be an acute-angled triangle and let D,E,F D,E,F be the feet of perpendiculars from A,B,C A,B,C respectively to BC,CA,AB. BC,CA,AB . Let the perpendiculars from F F to CB,CA,AD,BE CB,CA,AD,BE meet them in P,Q,M,N P,Q,M,N respectively. Prove that the points P,Q,M,N P,Q,M,N are collinear.
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