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Capture the Flag (Posted on 2008-05-04) Difficulty: 4 of 5

Let O designate the centre of an equilateral triangle. Points U-Z are chosen at random within the triangle. We have learnt that points U,V,W are each nearer to a (possibly different) vertex than to O; while X,Y are each closer to O than to any of the vertices.

Show that triangle XYZ is more likely than triangle UVW to contain the point O within its interior.

See The Solution Submitted by FrankM    
Rating: 3.5000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): Extra Credit (Triangle XUV)Charlie2008-05-09 12:12:35
Some Thoughtsre(2): Extra Credit (Triangle XUV)Steve Herman2008-05-08 22:28:49
re: Extra Credit (Triangle XUV)Charlie2008-05-08 10:29:18
Extra Credit (Triangle XUV)Steve Herman2008-05-07 23:35:23
A remarkable insightFrankM2008-05-07 06:13:20
SolutionThe missing insightSteve Herman2008-05-06 19:54:39
Not foolish at allFrankM2008-05-05 22:42:50
Some ThoughtsFools rush in where wise men fear to go (spoiler)Steve Herman2008-05-05 22:30:23
Very pretty (so far)FrankM2008-05-05 06:01:22
Solutionsemi-analytic; semi-computerCharlie2008-05-04 18:26:16
Hints/TipsSolving UVW (partial spoiler)Steve Herman2008-05-04 15:26:12
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