Three circles touch each other externally. A triangle is formed when the centers of these circles are joined together. Find the sum of the radii of the three circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.

23 cm

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11.5 cm

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46 cm

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30 cm

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Solution

The correct option is B 11.5 cm

AB = 6 cm, AC = 8 cm and BC = 9 cm

Let radii of the circles having centers A, B and C be r1, r2 and r3 respectively.

r1 + r3 = 8

r3 + r2 = 9

r2 + r1 = 6

Adding

r1 + r3 + r3 + r2 + r2 + r1 = 8+9+6

2(r1 + r2 + r3) = 23

r1 + r2 + r3 = 11.5 cm

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Three circles touch each other externally. A triangle is formed when the centers of these circles are joined together. Find the sum of the radii of the three circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.

The correct option is B 11.5 cm AB = 6 cm, AC = 8 cm and BC = 9 cm Let radii of the circles having centers A, B and C be r1, r2 and r3 respectively. r1 + r3 = 8 r3 + r2 = 9 r2 + r1 = 6 Adding r1 + r3 + r3 + r2 + r2 + r1 = 8+9+6 2(r1 + r2 + r3) = 23 r1 + r2 + r3 = 11.5 cm

The correct option is B 11.5 cm

AB = 6 cm, AC = 8 cm and BC = 9 cm

Let radii of the circles having centers A, B and C be r1, r2 and r3 respectively.

r1 + r3 = 8

r3 + r2 = 9

r2 + r1 = 6

Adding

r1 + r3 + r3 + r2 + r2 + r1 = 8+9+6

2(r1 + r2 + r3) = 23

r1 + r2 + r3 = 11.5 cm