This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2006 Mathematics for Its Sake, 3
Tags: geometry , discrete math , discrete geometry , g.m. , pigeonhole principle
Show that if the point $ M $ is situated in the interior of a square $ ABCD, $ then, among the segments $ MA,MB,MC,MD, $ [b]a)[/b] at most one of them is greater with a factor of $ \sqrt 5/2 $ than the side of the square. [b]b)[/b] at most two of them are greater than the side of the square. [b]c)[/b] at most three of them are greater with a factor of $ \sqrt 2/2 $ than the side of the square.