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Math Help - nine point circle proof

  1. #1
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    nine point circle proof

    If a side of Triangle ABC is tangent to its nine- point circle then triangle ABC is isosceles.

    How do I prove this?
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  2. #2
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
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    The nine point circle passes through the midpoints of the sides and the feet of the altitudes, so if it's tangent to a side, the altitude to that side is the perpendicular bisector of that side. I think you can go from there.
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