Problem

Source: Romanian TST 2007, Day 6, Problem 2

Tags: geometry, trigonometry, AMC, USA(J)MO, USAJMO, perpendicular bisector, geometry proposed



Let ABC be a triangle, let E,F be the tangency points of the incircle Γ(I) to the sides AC, respectively AB, and let M be the midpoint of the side BC. Let N=AMEF, let γ(M) be the circle of diameter BC, and let X,Y be the other (than B,C) intersection points of BI, respectively CI, with γ. Prove that NXNY=ACAB. Cosmin Pohoata