    Question

# Three circles touch each other externally. The distance between their centres 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 C 2 cm, 3 cm, 4 cmConsider the below figure 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) y+z=6 .....(2) (⇒y=6-z)... (2.1) 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=9⇒z=4 Now using, (3) ⇒x=7−z=7−4=3 And (2.1) ⇒y=6−z=6−4=2 Therefore, the radii of the circles are 3 cm, 2 cm and 4 cm.  Suggest Corrections  0      Similar questions  Related Videos   Introduction to Circles
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