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Last edited by hbghlyj 2025-3-19 21:13D在BC上, E在AB上, F为AD与BC的交点, 则
1area (△ AEC) + 1area (△ ADC) = 1area (△ AFC) + 1area (△ ABC).
来源Wikipedia
证明\[{\S{AFC}\over\S{AEC}}+{\S{AFC}\over\S{ADC}}={\S{AFBC}\over\S{ABC}}+{\S{ABFC}\over\S{ABC}}=1+{\S{AFC}\over\S{ABC}}\]
当$AE\px CD$时, $\frac1{\S{ABC}}=0$, 得到crossed ladders theorem |
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