midpoint wanted, perp. bisectors (2020 Novosibirsk Oral Geo Oly 8.5)
Source:
May 20, 2021
geometryperpendicular bisectormidpoint
Problem Statement
Line is perpendicular to one of the medians of the triangle. The median perpendiculars to the sides of this triangle intersect the line at three points. Prove that one of them is the midpoint of the segment formed by the other two.