midpoint and base of altitude symmertic wrt touchpoint with incircle
Source: 2009 Sharygin Geometry Olympiad Final Round problem 1 grade 9
July 26, 2018
geometryperimetersymmetry
Problem Statement
The midpoint of triangle's side and the base of the altitude to this side are symmetric wrt the touching point of this side with the incircle. Prove that this side equals one third of triangle's perimeter.(A.Blinkov, Y.Blinkov)