Theorem 3.14: If two circles have the same radius, then the points of intersection between the two circles lie on the perpendicular bisector of the line segment joining the two centers.

Proof: In Theorem 3.12, we noted that the line containing the points of intersection is perpendicular to the line joining the centers. If the radii of the circles are the same, then the formulae in Theorem 3.13 simplify to the formulae for the coordinates of the midpoint of the line segment between the centers.

next theorem (3.15)