Automatic Proving Facilities of Cinderella

Activity Problem

In the opposite figure, What can you say about the three points F, C, and E in terms of collinearity? i.e. Are they collinear?
Please enable Java for an interactive construction (with Cinderella).
Drag free elements (free points (A and B), semi free points (C and D), or even the edge of either circle) to deform the situation and make a conjecture about the behavior of the three points F, C, and E in terms of the collinearity.