The Perpendicular Theorem
If H is an h-line, then,
for any point P, there is a unique h-line through P perpndicular to H.
As usual, we take the h-inversion t mapping P to O.
We show that there is a unique h-line K through O (i.e a diameter of C)
perpendicular to t(H).
Since inversions preserve angles, t-1(K) is the required h-line.
First suppose that P lies on H.
Now suppose that P does not lie on H.