MathDB
a probably new characterization of AC/AB

Source: Romanian TST 2007, Day 6, Problem 2

June 8, 2007
geometrytrigonometryAMCUSA(J)MOUSAJMOperpendicular bisectorgeometry proposed

Problem Statement

Let ABC ABC be a triangle, let E,F E, F be the tangency points of the incircle Γ(I) \Gamma(I) to the sides AC AC, respectively AB AB, and let M M be the midpoint of the side BC BC. Let N \equal{} AM \cap EF, let γ(M) \gamma(M) be the circle of diameter BC BC, and let X,Y X, Y be the other (than B,C B, C) intersection points of BI BI, respectively CI CI, with γ \gamma. Prove that \frac {NX} {NY} \equal{} \frac {AC} {AB}. Cosmin Pohoata
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