The Perpendicular Theorem
If H is an hline, then, for any point P, there is a unique hline through P perpndicular to H.


Proof As usual, we take the hinversion t mapping P to O. We show that there is a unique hline K through O (i.e a diameter of C) perpendicular to t(H). Since inversions preserve angles, t^{1}(K) is the required hline.
First suppose that P lies on H.
Now suppose that P does not lie on H.
