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Question

Three circles touch each other externally. The distance between their centers is 5 cm, 6 cm and 7 cm. Find the radii of the circles.

A
2 cm,3 cm,4 cm
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B
3 cm,4 cm,1 cm
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C
1 cm,2.5 cm,3.5 cm
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D
1 cm,2 cm,4 cm
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Solution

The correct option is A 2 cm,3 cm,4 cm
Consider the given image wherein three circles touch each other externally.

Since the distances between the centres of these circles are 5 cm,6 cm and 7 cm respectively, we have the following set of equations with respect to the above diagram
x+y=5 .......(1)
z+y=6 .......(2)
x+z=7 .......(3)
Adding (1), (2) and (3), we have
2(x+y+z)=5+6+7=18
x+y+z=9 .......(4)
Using (1) in (4), we have
5+z=9z=4
Now using, (3)x=7z=74=3
And y=6z=64=2
Therefore, the radii of the circles are 3 cm,2 cm and 4 cm

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