MathDB
Iran NMO 2008 (Second Round) - Problem2

Source:

September 22, 2010
geometryincentertrigonometrypower of a pointradical axisgeometry proposed

Problem Statement

Let IaI_a be the AA-excenter of ΔABC\Delta ABC and the AA-excircle of ΔABC\Delta ABC be tangent to the lines AB,ACAB,AC at B′,C′B',C', respectively. IaB,IaC I_aB,I_aC meet B′C′B'C' at P,QP,Q, respectively. MM is the meet point of BQ,CPBQ,CP. Prove that the length of the perpendicular from MM to BCBC is equal to rr where rr is the radius of incircle of ΔABC\Delta ABC.
Back to ProblemsView on AoPS