Three circles touch each other externally. The distance between their centres is $5 c m, 6 c m$ and $7 c m .$ 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 option is
B

2 cm, 3 cm, 4 cm

In the figure, let $A B = 5 c m, B C = 6 c m$ and $A C = 7 c m$

$A B = x + y = 5$ …..(i)
Also

$B C = y + z = 6$
$\Rightarrow y = 6 - z$

Substituting in (i), we get,

$x + 6 - z = 5$

$\Rightarrow x - z = - 1$ …..(ii)

Also, $A C = x + z = 7$ …..(iii)

Adding (ii) and (iii), we get,

$2 x = 6 \Rightarrow x = 3, ∴ y = 2, z = 4$

Therefore, the radii of the circle is $2, 3$ and $4 c m$

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