In article <3gs4ue$qts@news.ysu.edu> of rec.puzzles, Matthew Buas <aq271@yfn.ysu.edu> wrote: 

                        A
                      //\
                 /  /  /|\
             /     /  / | \
         /       /   /  |  \
      /         /   /   |   \
    C---------/----/----|----\B
              M   K      D

Given: triangle ABC; altitude AD; angle bisector AK; median AM angle CAM=MAK=KAD=DAB (all the four smaller angles forming BAC are equal)

Prove: angle BAC is a right angle

[excuse the inaccuracy of the drawing]

2/2/95

Matt Buas

<send proofs to <mbuas@cap.gwu.edu>

-this is a really interesting problem, it took me a long while to solve, i'd be curious to see different proofs

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