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)]. Please WAIT while the applet loads. NOTE: If a security pop-up menu appears in your browser, please choose RUN/ALLOW to let the GeoGebra applet run properly. It is completely safe & can be trusted. Drag points A, B, C, D or E and observe the theorem dynamically.
Michael de Villiers, 12 March 2012, created with GeoGebra |