Show that the circles having equations \(x^2 + y^2 = 25\) and \(x^2 + y^2 - 24x - 18y + 125 = 0\) touch each other. Calculate the coordinates of the point at which they touch.

Could I sketch the two circles and observe what is happening?

If the two circles touch, then in how many points do they intersect?

Could we solve the two equations simultaneously?

How could I do this as neatly as possible, and how many solutions would I expect?