MathDB
perpendicular bisects MN - VI Soros Olympiad 1999-00 Round 1 10.7

Source:

May 21, 2024
geometrybisects segment

Problem Statement

Let a line, perpendicular to side ADAD of parallelogram ABCDABCD passing through point BB, intersect line CDCD at point MM, and a line, passing through point BB and perpendicular to side CDCD, intersect line ADAD at point NN. Prove that the line passing through point BB perpendicular to the diagonal ACAC, passes through the midpoint of the segment MNMN.