The Relationship between the Line of Centers and the Common Chord

Conjecture 1

The line segment AB is the perpendicular bisector of the line segment CD.










Hint

The line of centers of two intersecting circles is perpendicular to the common chord and bisects it.

 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 check correctness of the conjecture.