The Line of Centers as an Angular Bisector

Conjecture 4

The line segment AB bisects the two angles:
DBC and DAC.

i.e. m(∠DBA) = m(∠ABC) and

     m(∠DAB) = m(∠BAC)		 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.