



 
Carley, First draw a neat figure and label the orthocenters A’, B’, C’, and D’, where A’ is the orthocenter of the triangle BCD that leaves A out, and so on. Can you prove that the sides of the new quadrilateral A’B’C’D’ are parallel to the corresponding sides of the given quadrilateral? (By that I mean A’B’ is parallel to AB, and so on.) If you can, then it shouldn’t be too hard to prove that the segments AA’, BB’, CC’, and DD’ all have a common midpoint. Chris  


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