Problem

Source: Romanian JBMO TST 2005 - day 2, problem 3

Tags: geometry, algebra, polynomial



Let ABC be an equilateral triangle and M be a point inside the triangle. We denote by A, B, C the projections of the point M on the sides BC, CA and AB respectively. Prove that the lines AA, BB and CC are concurrent if and only if M belongs to an altitude of the triangle.