Given Points:
The points given are (1, 2), (5, 2), and (5, -2).

Center of the Circle:
To find the center of the circle, we need to find the intersection point of the perpendicular bisectors of any two chords formed by the given points.

Midpoints:
First, we find the midpoints of the chords formed by the given points:
- Midpoint of (1, 2) and (5, 2) = ((1+5)/2, (2+2)/2) = (3, 2)
- Midpoint of (1, 2) and (5, -2) = ((1+5)/2, (2-2)/2) = (3, 0)

Perpendicular Bisectors:
Next, we find the equations of the perpendicular bisectors of the chords formed by the given points:
- Perpendicular bisector of (1, 2) and (5, 2):
- Slope of the chord = (2-2)/(1-5) = 0
- Slope of the perpendicular bisector = -1/0 (perpendicular to a line with slope 0)
- Equation of the perpendicular bisector passing through (3,2): x = 3

- Perpendicular bisector of (1, 2) and (5, -2):
- Slope of the chord = (-2-2)/(5-1) = -1
- Slope of the perpendicular bisector = 1/1 (negative reciprocal of -1)
- Equation of the perpendicular bisector passing through (3,0): y = x - 3

Intersection Point:
Now, we find the intersection point of the two perpendicular bisectors:
- Since the equation of the first perpendicular bisector is x = 3, the x-coordinate of the intersection point is 3.
- Substituting x = 3 into the equation of the second perpendicular bisector, we get y = 3 - 3 = 0.
- Therefore, the intersection point is (3, 0).

Radius:
The radius of the circle passing through the given points is the distance from the center (3, 0) to any of the given points. Let's calculate the distance from (3, 0) to (1, 2):
- Distance = sqrt((1-3)^2 + (2-0)^2) = sqrt(4+4) = sqrt(8) = 2sqrt(2)

Final Answer:
The radius of the circle passing through the points (1, 2), (5, 2), and (5, -2) is 2sqrt(2).