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 4-gon Probability (Posted on 2006-11-03)
Points A, B, C, and D (no three of which are collinear) lie in a plane. If point D lies randomly within ΔABC's anticomplementary triangle, then what is the probability that 4-gon ABCD is (concave, convex, reflex)?

What would be the answer if ΔABC is equilateral and "ΔABC's anticomplementary triangle" is replaced with "ΔABC's circumcircle"?

NOTE: The anticomplementary triangle of a given triangle is formed by three lines. Each line passes through a vertex of the given triangle and is parallel to the opposite side.

NOTE: The circumcircle of a given triangle is the unique circle which passes through each of its vertices.

 See The Solution Submitted by Bractals Rating: 3.2500 (4 votes)

 Subject Author Date Part 1 is simpler. Jer 2006-11-03 11:37:43 outline of part 1; solution part 2 Charlie 2006-11-03 09:55:11

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