MathDB

2

Part of 2019 Mexico National Olympiad

Problems(1)

Perpendicular lines CM and BF in orthocenter configuration

Source: Mexico National Olympiad 2019 Problem 2

11/12/2019
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
geometryorthocenterperpendicular linesperpendicular bisector