MathDB
Cono Sur Shortlist 2012, Problem G5

Source:

August 23, 2014
geometryincentergeometry proposed

Problem Statement

Let ABCABC be an acute triangle, and let HAH_A, HBH_B, and HCH_C be the feet of the altitudes relative to vertices AA, BB, and CC, respectively. Define IAI_A, IBI_B, and ICI_C as the incenters of triangles AHBHCAH_B H_C, BHCHABH_C H_A, and CHAHBCH_A H_B, respectively. Let TAT_A, TBT_B, and TCT_C be the intersection of the incircle of triangle ABCABC with BCBC, CACA, and ABAB, respectively. Prove that the triangles IAIBICI_A I_B I_C and TATBTCT_A T_B T_C are congruent.
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