The locus of the Intersection Point of Angular Bisectors of a Triangle

Conjecture The locus of the intersection point of angular bisectors of the interior angles of a triangle is an algebric curve of higher degree.	Please enable Java for an interactive construction (with Cinderella).
	Drag the free elements, move the point C along the straight line L, or use the animation buttons to experience the locus of the intersection point of angular bisectors of the interior angles of a triangle.