Given 2 outer points of a perfect circle, find the centerpoint

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Alright, I hope this makes some sense.

I am using a software that can create arcs. This arc is defined by: Begin point End point Center of "circle"

The center is supposed to be the center of the imaginary circle that these two points bind to.

Here is a bad picture: enter image description here

I know p1 and p2. I know the circle is a perfect circle. I have no idea what the proper way to get the circle midpoint is!