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.

2 cm, 3 cm, 4 cm

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3 cm, 4 cm, 1 cm

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1 cm, 2.5 cm, 3.5 cm

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1 cm, 2 cm, 4 cm

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Solution

The correct options are
A
2 cm, 3 cm, 4 cm

B
3 cm, 4 cm, 1 cm

D
1 cm, 2 cm, 4 cm

Given, three circles with centres A, B and C respectively.

Let 'x', 'y' and 'z' be the radius of circle with centre A, B and C respectively.

From the figure,

x+y=5 (given) …..(i)

y+z=6 (given)

$\Rightarrow$ y=6-z

Substituting y in (i), we get

x+6-z=5

x-z=-1 …..(ii)

x+z=7 (given) …..(iii)

Adding (ii) and (iii), we get

2x = 6
x = 3 cm
y= 5 - x = 5 - 3 = 2 cm

z= 6 - y = 6 - 2 = 4 cm

Therefore, the radii of the circles are 2 cm, 3 cm and 4 cm respectively.

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