austrian midpoint, incircle and perpendiculars related
Source: 47th Austrian Mathematical Olympiad National Competition (Final Round, part 2, first day) May 25, 2016 p2
May 25, 2019
geometrymidpointincircleperpendicular
Problem Statement
Let be a triangle. Its incircle meets the sides and in the points and , respectively. Let denote the intersection point of and the line perpendicular to and passing through , and similarly let denote the intersection point of and the line perpendicular to and passing through .
Prove that is the mid-point of the segment .Proposed by Karl Czakler