How is the area of a triangle related to the circumcircle of that triangle?

Click here for GSP 4.0 sketch to manipulate/explore:

Click here for a generous hint as to the relationship you are intended to recognize. (If your conjecture differs from the one implied by this sketch, please let me know (kmealor5@hotmail.com).

Try proving this conjecture on your own, then compare your efforts with this proof.