###### Online 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 solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
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