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 Capture the Flag (Posted on 2008-05-04)

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)

 Subject Author Date re(3): Extra Credit (Triangle XUV) Charlie 2008-05-09 12:12:35 re(2): Extra Credit (Triangle XUV) Steve Herman 2008-05-08 22:28:49 re: Extra Credit (Triangle XUV) Charlie 2008-05-08 10:29:18 Extra Credit (Triangle XUV) Steve Herman 2008-05-07 23:35:23 A remarkable insight FrankM 2008-05-07 06:13:20 The missing insight Steve Herman 2008-05-06 19:54:39 Not foolish at all FrankM 2008-05-05 22:42:50 Fools rush in where wise men fear to go (spoiler) Steve Herman 2008-05-05 22:30:23 Very pretty (so far) FrankM 2008-05-05 06:01:22 semi-analytic; semi-computer Charlie 2008-05-04 18:26:16 Solving UVW (partial spoiler) Steve Herman 2008-05-04 15:26:12

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