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The points $(-3,2)$ and $(-2,3)$ lie on a circle whose center is on the $x$-axis. What is the radius of the circle?

If the center lies on the x axis, let the center be (x, 0)

So....the distance from the center to either point will be the same...so

( -3 - x)^2 + (2 - 0)^2  =  (-2 - x)^2 + ( 3 - 0)^2

x^2 + 6x + 9  + 4  =  x^2 + 4x + 4 + 9

6x + 13  = 4x + 13

2x  = 0

x = 0

So...the center is at the origin  ....so the radius is

√ (-3)^2 + (2)^2  ]  =

√ [9 + 4]

√13