Elementary set theory problem

[Townsend]

Let C be a circle and let D be the set of all diameters of C. What is \capD?


I think it is the center of the circle since that would be the only point of intersection of all the diameters of the circle. Could someone let me know if I am correct?

Regards

Jeremy

[Hurkyl]

Do you have any thoughts as to how you could go about proving it?