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3 circles with centers A, B, C and radii AH, BH, CH have a common tangent

Source: 2014 Sharygin Geometry Olympiad Final Round 9.4

August 3, 2018
common tangentscirclesgeometry

Problem Statement

Let HH be the orthocenter of a triangle ABCABC. Given that HH lies on the incircle of ABCABC , prove that three circles with centers A,B,CA, B, C and radii AH,BH,CHAH, BH, CH have a common tangent.
(Mahdi Etesami Fard)
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