How to construct the circumcenter of a triangle using a compass ONLY.

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I just figured out how to find the midpoint between two points using just a compass and no straight edge. A similar approach can be found in this question:

Constructing the midpoint of a segment by compass

Now what I am wondering is, can I find the circumcenter of a scalene triangle using just a compass and no straight edge?

I am thinking of drawing a perpendicular at C (in the diagram in the link of the answer presented by commenter and has nine likes) and choosing more points as my centres on that line to create a circle with points A and M on it. So in essence, I would be transforming a line (the perpendicular) into a circle, which I can draw using a compass. Yet, I do not really know if and how it helps.

Best of luck!

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