Nickalls' Theorem (hyperbola case)
If tangents from two points E and D are drawn to a hyperbola with foci A and B, and these tangents respectively intersect at F and G as shown below, and all angles are measured in the same direction (e.g. anti-clockwise), then ∠EFD - ∠EGD = ∠EBD - ∠EAD [or as shown by the dynamic measurements on the bottom left β - α (= ε) = δ - γ (= ζ)].
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Drag points A, B, C, D or E and observe the theorem dynamically.
Michael de Villiers, 12 March 2012, created with GeoGebra