Circumferential angles

 
A, B, C are lying on a circle with the center M. They form the triangles ABC and ABM.

a) What do you notice about the marked angles at C and M?
b) Vary the triangles by dragging at C (at A, B). What do you notice? Explain! 
c) What can you say about the other angles at C and M?
d) The center-angle at M is constant, when you vary C. 
    What can you conclude for the circumferential angle at C?
 

hint (if necessary)

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