Ellipse in a Circle Locus

Given: point C is a point on circle O. point F is a point inside circle O. line DL is the perpendicular bisector of FC. point L is on radius OC. As point C moves around circle O, point L moves. What is its locus? Why is its locus what it is? Click the box to the left of "Show Trace of point L" to trace point L. Click the box to the left of "Show Locus of point L" to see the locus of point L. Click the play/pause botton in the lower left to start/stop animating point C. Move point F around to see how the locus changes.