Three circles touch each other externally. The distance between their centre 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 option is A 2 cm, 3 cm, 4 cm
AB = 5 cm = x + y
BC = 6 cm = y + z
AC = 7 cm = z + x

$∴$ 2(x + y + z) = 5 + 6 + 7 = 18 cm
$∴$ x + y + z = 9 cm
$∴$ x = (x + y + z) - (y + z) = 9 - 6 = 3 cm
$∴$ x + y = 5 cm
$∴$ y = 5 - x = 5 - 3 = 2 cm
$∴$ z = 6 - y = 6 - 2 = 4 cm
$∴$ x = 3 cm
y = 2 cm and z = 4 cm

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