MathDB
Perpendicular lines CM and BF in orthocenter configuration

Source: Mexico National Olympiad 2019 Problem 2

November 12, 2019
geometryorthocenterperpendicular linesperpendicular bisector

Problem Statement

Let HH be the orthocenter of acute-angled triangle ABCABC and MM be the midpoint of AHAH. Line BHBH cuts ACAC at DD. Consider point EE such that BCBC is the perpendicular bisector of DEDE. Segments CMCM and AEAE intersect at FF. Show that BFBF is perpendicular to CMCM.
Proposed by Germán Puga
Back to ProblemsView on AoPS