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    Re: A simple three-body fix puzzle
    From: UNK
    Date: 2010 Dec 10, 21:08 +0000

    The correct solution for the MPP is in your second diagram, exactly 
    where you circled it. All you needed to do was to drop the altitude from 
    P onto the hypotenuse and bisect it. This is the so-called symmedian 
    point or Lemoine point.
    The Gergonne point has nothing to do with our problem.  It is NOT the 
    symmedian point.
    On 2010-12-10 20:32, Greg Rudzinski wrote:
    > Herbert,
    > Could you inspect and comment on the linked diagrams.
    > The first linked diagram shows a 30°/60°/90° triangle plot with 
    > bisected vertex, internal circle tangents, vertex to tangent 
    > intersections (symmedian or Gergonne point), and the d/2 circle around 
    > point P.
    > (very busy plot)
    > The Gergonne point (Gp) seems to be dependent on the bisected angle 
    > point (Bp). Point Bp weighs each LOP equally and point Gp shifts away 
    > from the smallest angle and toward the largest angle. The d/2 circle 
    > intersects at three points along the bisection and tangent lines.
    > The question now is which point is correct ? Gp or one of the three 
    > d/2 intersections ? If I had to guess then I would select the 
    > intersection of the d/2 circle, P perpendicular, and 60° vertex to 
    > inner circle tangent (see second linked diagram)
    > Greg Rudzinski
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