1. ## Set of incentres

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

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?

2. Originally Posted by pinkparrot
Points: $\displaystyle A, B$ belong to the circle $\displaystyle k$. Find the set of the incentres of all triangles $\displaystyle ABP$ where $\displaystyle P \in k$.

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.

3. 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