MathDB
perp. bisector of NM bisects AB, altitudes (2020 Novosibirsk Oral Geo Oly 7.4)

Source:

April 27, 2021
geometrybisects segment

Problem Statement

The altitudes ANAN and BMBM are drawn in triangle ABCABC. Prove that the perpendicular bisector to the segment NMNM divides the segment ABAB in half.