Thread: Complex Circle Geometry
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Old May 24th, 2009, 04:12 AM
Laurent Laurent is offline
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Quote:
Originally Posted by Opalg View Post
In fact, the correct condition is a combination of those two. If B and D are on the same side of AC then angle(ABC)=angle(ADC). If they are on opposite sides then angle(ADC)+angle(ABC)=π. In either case, the cross-ratio is real. In one case it is positive and in the other case it is negative.
Thank you, Opalg, for this reminder.

Now I remember, a unifying condition is (with oriented angles): \widehat{ABC}\equiv\widehat{ADC}\!\!\!\pmod{\pi} (i.e. (\overrightarrow{BA},\overrightarrow{BC})\equiv (\overrightarrow{DA},\overrightarrow{DC})\!\!\!\pmod{\pi}.)
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