Problem

Source: 2014 Sharygin Geometry Olympiad Final Round 9.4

Tags: common tangents, circles, geometry



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