初三几何题(相似形相关)
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初三几何题(相似形相关)
在△ABC中,DE∥AB,DF∥AC,且S□afde=12/25S△abc,求BD:DC的值
![](http://img.wesiedu.com/upload/f/1b/f1bd06f240b5fe1394a393f7080a58ce.jpg)
在△ABC中,DE∥AB,DF∥AC,且S□afde=12/25S△abc,求BD:DC的值
![](http://img.wesiedu.com/upload/f/1b/f1bd06f240b5fe1394a393f7080a58ce.jpg)
![初三几何题(相似形相关)](/uploads/image/z/261388-28-8.jpg?t=%E5%88%9D%E4%B8%89%E5%87%A0%E4%BD%95%E9%A2%98%EF%BC%88%E7%9B%B8%E4%BC%BC%E5%BD%A2%E7%9B%B8%E5%85%B3%EF%BC%89)
∵DE∥AB,DF∥AC
∴△FBD∽△EDC∽△ABC
S△FBD=BD²/BC²*S△ABC
S△EDC=DC²/BC²*S△ABC
S△FBD+S△EDC+S□AFDE=S△ABC
BD²/BC²*S△ABC+DC²/BC²*S△ABC+12/25S△ABC=S△ABC
BD²/BC²+DC²/BC²=13/25
25(BD²+DC²)=13BC²=13(BD+DC)²
6BD-13BD*DC+6DC²=0
(3BD-2DC)(2BD-3DC)=0
∴BD/DC=3/2,或BD/DC=3/2
∴△FBD∽△EDC∽△ABC
S△FBD=BD²/BC²*S△ABC
S△EDC=DC²/BC²*S△ABC
S△FBD+S△EDC+S□AFDE=S△ABC
BD²/BC²*S△ABC+DC²/BC²*S△ABC+12/25S△ABC=S△ABC
BD²/BC²+DC²/BC²=13/25
25(BD²+DC²)=13BC²=13(BD+DC)²
6BD-13BD*DC+6DC²=0
(3BD-2DC)(2BD-3DC)=0
∴BD/DC=3/2,或BD/DC=3/2