Question 939801
A and B are both the same distance from the center of the circle.  The given line contains the center of the circle, the line also being equivalent to y=x+1, means the center of the circle is a variable point (x,x+1).


Setup a relationship of distances:


{{{sqrt((x-(-2))^2+(x+1-4)^2)=sqrt((x-7)^2+(x+1-7)^2)}}}


If that makes sense, then you understood about half the solution process.
Simplify; put into standard form, identify the radius value.