The points $(0,4)$ and $(1,3)$ lie on a circle whose center is on the $x$-axis. What is the radius of the circle?

Notice if the  center is on the  x axis...it must have the coordinates of  (a, 0)

Because the  distance  from each point to  the  center is the  same we  can solve for a  thusly :

(a-0)^2  + (0 - 4)^2   =  ( a -1)^2  + ( 0 -3)^2    simplify

a^2  + 16 = a^2  -2a + 1  + 9     subtract a^2  from both sides

16  = -2a + 10

16 - 10  = -2a

6 = -2a

6/-2 =  a

-3  = a

Coordinates of center=  (-3,0)

Radius =  sqrt [ (-3 - 0)^2   + (4 - 0)^2  ]  =  sqrt [ 9 + 16 ] =  sqrt 25  =  5

Here's a graph :   https://www.desmos.com/calculator/cu9ityz6lb