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.
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Proof 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.
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