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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.
题目详情
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.
Three unit circles are arranged so that each touches the other two .Find the radii of the two circles which touch all three.
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答案和解析
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.
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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