Geometry Problem 870: Triangle, Median, Three Squares, Centers,
Vertices, Collinear Points, Midpoint. Level: High School,
The figure below shows a triangle ABC with
the median BN. If ABDE, BFGN, and BHMC are squares of centers O1, O2, and O3, respectively, prove
that (1) F is the midpoint of DH, (2) G is the midpoint of EM, (3) O2,
is the midpoint of O1O3.