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Math Help - Set of incentres

  1. #1
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    Set of incentres

    Points: A, B belong to the circle k. Find the set of the incentres of all triangles ABP where P \in k.


    I assume the set is an ellipse (excluding the points A and B). If so, how can I prove that and is it ever possible to find its equation?
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  2. #2
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    Quote Originally Posted by pinkparrot View Post
    Points: A, B belong to the circle k. Find the set of the incentres of all triangles ABP where P \in k.


    I assume the set is an ellipse (excluding the points A and B). If so, how can I prove that and is it ever possible to find its equation?
    I've sketched the circle k (black) and 3 triangles (blue) with their incenters.

    The locus of all incenters if P is moving on the circle line is sketched in red.

    I cann't provide you with an equation of the curve.
    Attached Thumbnails Attached Thumbnails Set of incentres-ortskurve_w.png  
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  3. #3
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    Thanks for the graph, it now turns out that it's not an ellipse at all... Could be 2 parabolae or arcs instead. Any help on defining the curves and, if possible, giving their equations would be appreciated
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