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[几何] 圆内接六边形证共线

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hbghlyj Posted 2025-4-13 08:48 |Read mode

圆内接六边形ABCDEF,AB交DF于J，类似得到点K,L,G，JL交KG于M，过点E,F的圆的切线分别交CA,BA于N,P，求证: N,P,M共线

帕斯卡定理

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星奔川骛 Posted 2025-4-13 12:47

实际上根本不难

设T=AD∩EF，对EEDACF使用Pascal定理得NGT共线，对FFDABE使用Pascal定理得PKT共线，对PJKNLG使用Desargues得PNM共线只需PJ∩NL,JK∩LG,PK∩NG共线即ADT共线，即证

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