segments of midpoints of incenters and excenters perpendicular to side
Source: 2018 Oral Moscow Geometry Olympiad grades 10-11 p4
July 25, 2019
geometrymidpointincenterexcenter
Problem Statement
On the side of the triangle , point is selected. In triangle point is the center of the inscribed circle, is the center of excircle wrt side . In the triangle point is the center of the inscribed circle, is the center of excircle wrt side . Prove that the line passing through the midpoints of the segments and is perpendicular to .