The average of the 3 points would give you the triangle's centroid, not necessarily its circumcenter. You can still calculate the circumradius from a, b, and c: https://mathworld.wolfram.com/Circumradius.html.

You could also use the law of cosines to get a triangle's angles pretty easily when you know its edge lengths: https://mathworld.wolfram.com/LawofCosines.html.