MathDB
midpoint wanted, perp. bisectors (2020 Novosibirsk Oral Geo Oly 8.5)

Source:

May 20, 2021
geometryperpendicular bisectormidpoint

Problem Statement

Line \ell is perpendicular to one of the medians of the triangle. The median perpendiculars to the sides of this triangle intersect the line \ell at three points. Prove that one of them is the midpoint of the segment formed by the other two.