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Trapped! (Posted on 2004-02-19) Difficulty: 4 of 5
Choose any four points in a plane, such that no three are collinear and the four do not lie on a circle.

Show that one of the points must lie within the circle formed by the other three.

See The Solution Submitted by DJ    
Rating: 4.4444 (9 votes)

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Some Thoughts Euler, Feuerbach, et. al. | Comment 4 of 9 |
I believe this problem is related to deep mathematical analysis involving the "nine point circle", which is the circle that can be constructed from any triangle in the plane. Of course I don't understand this well enough to copy/paste it without embarrassment, but greater minds than mine can read all about it at:

http://en.wikipedia.org/wiki/Nine_point_circle

:-)
  Posted by Penny on 2004-02-19 18:59:18
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