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[几何] 一个矩形和两个点

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hbghlyj posted 2021-3-15 22:58 |Read mode
Last edited by hbghlyj 2021-3-16 00:35 1639.png
点E,F在矩形ABCD的边上的投影为$E_i,F_i$.$E_2F_4$与AC,EF交于P,Q.过P作AB平行线,过Q作BC平行线交于R.点R在矩形的边上的投影为$R_i$,求证\[\overline{R_1 F_1}  \cdot\overline{R_1 B} + \overline{R_2 E_2} \cdot \overline{R_2 B}= \overline{R_4 F_4} \cdot\overline{R_4 D} + \overline{R_3 E_3}  \cdot\overline{R_3 D}\]

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