Question

The points (4,- 4) and (4,- 6) lie on a circle with a radius of 1. Find the center point of the circle.

Answer 1

If we intersect the circle of radius 1 around (4,-4) and the circle of radius 1 around (4,-6) they'll intersect at the center of circle radius 1 that has both those points.  

Here we don't really have to do any math.  It's clear that the midpoint (4,-5) is 1 away from both (4,-4) and (4,-6) so that's our answer:

Answer: (4,-5)