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Problem 501. Finsler–Hadwiger theorem. Triangle, Two Squares, Center, Midpoint, another Square. Level: High School, College, SAT Prep.

The drawing shows a triangle ABC with the squares ABDE and BCGH of centers F and N, respectively. If S and I are the midpoints of AC and DH, respectively, prove that FINS is another square.
 
 

Triangle, Three Squares, Centers, Midpoints
 
 
 

See also: Artwork of problem 501
 

 

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