MathDB
Polyline divides triangle into equal figures

Source: Kvant Magazine No. 2 2020 M2590

March 10, 2023
geometryareasKvant

Problem Statement

In an acute triangle ABCABC the point OO{} is the circumcenter, H1H_1 is the foot of the perpendicular from AA{} onto BCBC, and MHM_H and NHN_H are the projections of H1H_1 on ACAC and ABAB{}, respectively. Prove that the polyline MHONHM_HON_H divides the triangle ABCABC in two figures of equal area.
Proposed by I. A. Kushner