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    Re: Bisectors and MPP - for 3 sights, equivalent to circle method
    From: Bill Noyce
    Date: 2003 May 29, 14:11 -0400

    Doug Royer explains how to use angle bisectors to find
    the MPP for a round of three or four (or more?) sights,
    and wonders whether it's more or less precise than the
    method that finds a circle that just touches each LOP.
    
    For three sights, the three bisectors all meet at a point,
    which is also the center of the circle that will just
    touch each LOP.  Therefore, for three sights the methods
    are equivalent.
    
    To see this, imagine we have LOP's labeled A, B, and C,
    with bisectors AB, BC, and CA.  Consider the point
    where AB intersects BC.  Its distance from A is equal to
    its distance from B, because it is on bisector AB.  And
    its distance from B is equal to its distance from C,
    because it is on bisector BC.  Therefore its distance
    from A is equal to its distance from C, so it must also
    be on bisector CA.  The only point where all three
    distances are the same is the center of the circle that
    is tangent to all three bisectors (as long as we are on
    the proper side of each LOP, and both methods ensure that).
    
            -- Bill
    
    
    

       
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