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Problem 512: Triangle, Three Squares, Concurrency.
Level: High School, College, SAT Prep.

The drawing shows a triangle ABC with the squares ABDE, BCFG, and ACHJ. Lines ED and FG meet at M, GF and JH meet at N, DE and HJ meet at K. Prove that KA, MB, and NC are concurrent at a point P.

Triangle with squares and concurrency
 
 


 

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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