Find the locus of the points P within a given triangle ABC such that the distances from P to the sides of the given triangle can themselves be the sides of a certain triangle.
Let be the points where the angle bisectors at meet the opposite sides of the triangle. My guess is that the condition for P is that it must lie inside the triangle . I think (without having checked carefully) that I can prove this using coordinate geometry, but I don't see how to tackle it using euclidean methods.