Find the equation of the circumcircles of the triangle, whose vertices are A(2,3),B(5,4) and C(3,7)

Answer 1

There is only one circumcircle.
Find the perpendicular bisectors of two sides of ABC.
The center is where those two lines intersect.
the radius R = abc/4A where A is the area of ABC.

or, you can solve (x-h)^2 + (y-k)^2 = r^2
for all of the points.