MathDB
CGI is right iff GM // AB

Source: 2009 Sharygin Geometry Olympiad Final Round problem 6 grade 10

July 26, 2018
geometryCentroidincenterparallel

Problem Statement

Let M,IM, I be the centroid and the incenter of triangle ABC,A1ABC, A_1 and B1B_1 be the touching points of the incircle with sides BCBC and AC,GAC, G be the common point of lines AA1AA_1 and BB1BB_1. Prove that angle ∠CGI\angle CGI is right if and only if GM//ABGM // AB.
(A.Zaslavsky)
Back to ProblemsView on AoPS