求大神解一道挺难的几何题?
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/08/13 18:08:57
求大神解一道挺难的几何题?
![](http://img.wesiedu.com/upload/8/98/8986346240d4216b524907b73c3dbd6c.jpg)
如图
![](http://img.wesiedu.com/upload/8/98/8986346240d4216b524907b73c3dbd6c.jpg)
如图
![求大神解一道挺难的几何题?](/uploads/image/z/6666188-68-8.jpg?t=%E6%B1%82%E5%A4%A7%E7%A5%9E%E8%A7%A3%E4%B8%80%E9%81%93%E6%8C%BA%E9%9A%BE%E7%9A%84%E5%87%A0%E4%BD%95%E9%A2%98%3F)
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PF,PE为角平分线
设BP=x,AC=y
AP=4-x
CP/PA=CF/FA
CF=y/(5-x)
AF=(4-x)y/(5-x)
∵△APF∽△ACP
∴(4-x)^2=(4-x)y^2/(5-x)
y^2=(5-x)(4-x)
BC=√(16-y^2)
BP/PC=BE/EC
BE=x√(16-y^2)/(x+1)
∵△BPE∽△BCP
∴x^2=x(16-y^2)/(x+1)
x(x+1)=16-y^2
y^2=-x^2-x+16
-x^2-x+16=x^2-9x+20
2x^2-8x+4=0
x^2-4x+2=0
x=2±√2
∵∠BAC<45°
∴x=2-√2
AP/BP=(2+√2)/(2-√2)=3+2√2
有点麻烦