23rd Indian NMO ,08 Let $ABC $ be a triangle;$\lambda_A, \lambda_B,\lambda_C $ be three equal disjoint circles inside $ABC $ such that $\lambda_A $ touches $AB $ and $AC $ , $\lambda_B $ touches $BC $ and $BA $, $\lambda_C $ touches $CA $ and $CB $ . Let $\lambda $be a circle touching $\lambda_A, \lambda_B,\lambda_C $ externally. Prove that the line joining the circum-center $O $ and the in-center $I $ of triangle $ABC $ passes through the center of $\lambda $. [RIGHT][I][B]Nguồn: MathScope.ORG[/B][/I][/RIGHT] |