MathDB
incenter of ABC is orthocenter of triangles of excenters

Source: Indonesia INAMO Shortlist 2009 G10 https://artofproblemsolving.com/community/c1101409_

December 10, 2021
geometryincenterexcirclesexcenters

Problem Statement

Given a triangle ABCABC with incenter II . It is known that EAE_A is center of the ex-circle tangent to BCBC. Likewise, EBE_B and ECE_C are the centers of the ex-circles tangent to ACAC and ABAB, respectively. Prove that II is the orthocenter of the triangle EAEBECE_AE_BE_C.
Back to ProblemsView on AoPS