The locus of the Intersection Point of Perpendicular Bisector of a Triangle

Conjecture The locus of the intersection point of perpendicular bisectors of the sides of a triangle is a straight line, which is perpendicular to L the road line.	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 perpendicular bisectors of the sides of a triangle.