Three unit circles are arranged so that each touches the oth

来源：学生作业帮编辑：搜狗做题网作业帮分类：英语作业时间：2024/07/08 07:53:23

Three unit circles are arranged so that each touches the other two .Find the radii of the two ci...
Three unit circles are arranged so that each touches the other two .Find the radii of the two circles which touch all three.

Problem
Three unit circles are arranged so that each touches the other two.Find the radii of the two circles which touch all three.
Solution
The two circles have center at the center of the triangle,which is the centroid and hence a distance 2/3 √3 from the center of each of the unit circles.The two required radii are therefore 2/√3 ± 1.

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