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Posers and Puzzles

Posers and Puzzles

  1. 12 Mar '05 15:58
    In triangle ABC
    let side BC be of length a
    let side AC be of length b
    let side AB be of length c
    let P be a randomly chosen point inside ABC with uniform distribution

    What is the probability in terms of a,b,c that P will be:

    1) perpendicularly closer to side AB than it is to either of the other two sides?
    2) perpendicularly further from AB than the combined distances to the other two sides?
  2. 12 Mar '05 16:07
    Equal?!