The Locus of the Intersection Point of a Median and a Perpendicular Bisector of a Triangle

Conjecture

The locus of the intersection point of median and a perpendicular bisector is an algebraic 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 median and a perpendicular bisector of a triangle.