Theorem 3.11: The line joining the two points where two circles intersect is perpendicular to the line joining their centers.

Proof: If the line joining the centers is horizonal, then by Theorem 3.10, the line containing the centers is vertical. If not, then by Theorem 3.10, the slope of the line containing the solutions is

which is the negative recoprocal of the slope of the line joining the centers.

next theorem (3.12)