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Geometry Problem 870: Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint. Level: High School, College, Mathematics Education

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.
 

Geometry Problem 870: Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint
 

 

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