To find the center of a circle passing through three given points, we can use the concept of the perpendicular bisectors of the chords formed by these points. Let's break down the solution into the following steps:

Step 1: Find the equations of the perpendicular bisectors
1.1) First, let's find the midpoint of the line segment joining the points (7,-5) and (3,-7).
Midpoint formula: [(x1+x2)/2, (y1+y2)/2]
Midpoint = [(7+3)/2, (-5-7)/2]
= [5, -6]

1.2) Next, let's find the slope of the line joining the points (7,-5) and (3,-7).
Slope formula: (y2-y1)/(x2-x1)
Slope = (-7 - (-5))/(3 - 7)
= (-7 + 5)/(-4)
= -2/-4
= 1/2

1.3) The slope of the perpendicular bisector will be the negative reciprocal of the slope we obtained in step 1.2.
Slope of perpendicular bisector = -1/(1/2)
= -2

1.4) Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the midpoint, and m is the slope, we can substitute the values we obtained in steps 1.1 and 1.3 to find the equation of the perpendicular bisector.
Equation of the perpendicular bisector passing through the midpoint:
y - (-6) = -2(x - 5)
Simplifying, we get:
y + 6 = -2x + 10
y = -2x + 4

Step 2: Repeat steps 1.1 to 1.4 for the other two pairs of points
2.1) Midpoint of the line segment joining (7,-5) and (3,3):
Midpoint = [(7+3)/2, (-5+3)/2]
= [5, -1]

2.2) Slope of the line joining (7,-5) and (3,3):
Slope = (3 - (-5))/(3 - 7)
= 8/-4
= -2

2.3) Slope of the perpendicular bisector = -1/(-2) = 1/2

2.4) Equation of the perpendicular bisector passing through the midpoint:
y - (-1) = (1/2)(x - 5)
Simplifying, we get:
y + 1 = (1/2)x - (5/2)
y = (1/2)x - (5/2) - 1
y = (1/2)x - 7/2

3.1) Midpoint of the line segment joining (3,-7) and (3,3):
Midpoint = [(3+3)/2, (-7+3)/2]
= [3, -2]

3.2) Slope of the line joining (3,-7) and (3,3):
Slo