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Question

# In the figure given below AB = 7 cm BC = 8 cm CA = 5 cm. What are the radii of the circles A, B and C?

A

2 cm, 4 cm and 5 cm

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B

1 cm, 3 cm and 7 cm

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C

2 cm, 5 cm and 3 cm

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D

1 cm, 3 cm and 4 cm

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Solution

## The correct option is C 2 cm, 5 cm and 3 cm AB is nothing but sum of radii of circle A and circle B. Likewise for BC and CA. Let's try forming three simultaneous equations. The radii of circles with centres A, B and C are x, y and z respectively. x+y=7, y+z=8, z+x=5 ⇒y=8−z, Putting this value in x+y=7 ⇒x+8−z=7 ⇒x−z=−1 Also, x+z=5 Solving for x, y and z, we get x = 2 cm, y = 5 cm and z = 3 cm

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