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concurrent problem

Source: Baltic Way 2009

July 16, 2010
geometry unsolvedgeometry

Problem Statement

The point HH is the orthocentre of a triangle ABCABC, and the segments AD,BE,CFAD,BE,CF are its altitudes. The points I1,I2,I3I_1,I_2,I_3 are the incentres of the triangles EHF,FHD,DHEEHF,FHD,DHE respectively. Prove that the lines AI1,BI2,CI3AI_1,BI_2,CI_3 intersect at a single point.
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