题目内容
如图,三个半圆依次相外切,它们的圆心都在x轴上,并与直线OA相切,直线OA与x轴的夹角为30°.设三个半圆的半径依次为r1、r2、r3,则当r1=1时,r3= .![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408230139036965824.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408230139036965824.png)
9
由三个半圆依次与直线y=
x相切并且圆心都在x轴上,
∴y=
x倾斜角是30°,∴得,OO1=2r1,002=2r2=OO1+r1+r2=3r1+r2,003=2r3,
∴2r2=3r1+r2,∴r2=3r1,∵r1=1,∴OO1=2,002=2r2=6r1=6,003=18,∴r3=9.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013903696419.png)
∴y=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013903696419.png)
∴2r2=3r1+r2,∴r2=3r1,∵r1=1,∴OO1=2,002=2r2=6r1=6,003=18,∴r3=9.
![](http://thumb.zyjl.cn/images/loading.gif)
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