Points: belong to the circle . Find the set of the incentres of all triangles where . 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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Originally Posted by pinkparrot Points: belong to the circle . Find the set of the incentres of all triangles where . 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.

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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