**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.