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全面考虑数学问题（更新添加中----）

2012-04-14 17:22:49| 分类：试题集锦 | 标签： |举报 |字号大中小订阅

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1、将三角形纸片（ABC）按如图所示的方式折叠，使点B落在边AC上，记为点次B，折痕为EF.已知AB=AC=3,BC=4,若以点次B，F,C为顶点的三角形与ABC相似，那么BF的长度是________________.

解:如图,不妨设点B落在点D处.
⊿ABC中,AB=AC=3,BC=4;若⊿DFC与⊿ABC相似,则⊿DFC也为等腰三角形.设BF=X,则DF=BF=X;FC=4-X.
1)若FC=FD,则∠FDC=∠C=∠B,⊿FDC∽⊿ABC.
此时,FC=FD,即X=4-X,X=2.
2)若DC=DF,则∠DFC=∠C=∠B,⊿DFC∽⊿ABC.
此时,DF=DF=X,则DC/FC=AC/BC,X/(4-X)=3/4,X=12/7.
∴BF的长为2或12/7.

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