pcircle: If[isOrigin, c1, If[isCollinear, c3, c2]]
Hide all of the objects except A, B and pcircle and turn off the label for pcircle. Then use Tools/Create New Tool to create a custom tool, Pcircle, which accepts points A and B as inputs and outputs pcircle. Provide a helpful tooltip such as “Select center, then point” and create an icon for the tool if you wish.