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Analytic Proof, Geometry

  1. Jan 7, 2007 #1
    1. The problem statement, all variables and given/known data
    In triangle ABC, with vertices A(0,a), B(0,0) and C(b,c) prove that the right bisectors of the sides meet at a common point (the circumcentre).

    2. Relevant equations
    Midpoint(x1 + x2 / 2 , y1 + y2 / 2)
    Length of a Line

    3. The attempt at a solution
    I was thinking of using the Midpoints to prove that Midpoint AD = Midpoint BE = Midpoint CF.....is this the right way?
  2. jcsd
  3. Jan 7, 2007 #2


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    Gold Member

    Try finding the equations of the perpendicular bisectors.
  4. Jan 7, 2007 #3
    am i supposed to use new points D, E, and F? or should i use the circumcentre P?
  5. Jan 7, 2007 #4


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    Gold Member

    You can find the slopes of the lines that make up the 3 sides of the triangle, right? Once you do that, do you know how to find the slopes of lines perpendicular to each of these three lines?

    You also have one point on each of the bisectors: the midpoints of the sides of the triangles. Do you know a way of finding the equation of a line knowing its slope and one point on it?
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