With A, B, C as centres, three circles are drawn such that they touch each other externally. If the sides of the $△ A B C$ are $4 c m, 6 c m$ and $8 c m$ , then what is the sum of the radii of the circles?

9 c m

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10 c m

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12 c m

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14 c m

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Solution

The correct option is A $9 c m$
Let the radii of the three circles be x, y and z cms.
$\Rightarrow 2 x + 2 y + 2 z = (4 + 6 + 8) c m$
$\Rightarrow x + y + z = 9 c m$

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With A, B, C as centres, three circles are drawn such that they touch each other externally. If the sides of the △ABC are 4 cm,6 cm and 8 cm, then what is the sum of the radii of the circles?

The correct option is A 9 cmLet the radii of the three circles be x, y and z cms.⇒2x+2y+2z=(4+6+8)cm⇒x+y+z=9 cm

With A, B, C as centres, three circles are drawn such that they touch each other externally. If the sides of the $△ A B C$ are $4 c m, 6 c m$ and $8 c m$ , then what is the sum of the radii of the circles?

The correct option is A $9 c m$
Let the radii of the three circles be x, y and z cms.
$\Rightarrow 2 x + 2 y + 2 z = (4 + 6 + 8) c m$
$\Rightarrow x + y + z = 9 c m$