Hello, stewpot!

Your equations for the perpendicular bisectors are off . . .

Three points on a circle: .

Find the equation of the circle.

The midpoint of is: .

The slope of is: .

The perpendicular bisector of has point and slope

. . ts equation is: .

The midpoint of is: .

The slope of is: .

The pependicular bisector of has point and slope

. . Its equation is: .

Now try it . . .