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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 cmThe 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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