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- 1 cm - 3 cm and 4 cmB- 2 cm - 4 cm and 5 cmC- 1 cm - 3 cm and 7 cmD- 2 cm - 5 cm and 3 cm

In the figure...

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?

2 cm, 4 cm and 5 cm

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1 cm, 3 cm and 7 cm

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2 cm, 5 cm and 3 cm

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1 cm, 3 cm and 4 cm

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Solution

The correct option is D 2 cm, 5 cm and 3 cm
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
$\Rightarrow$ y = 8 - z, Putting this value in x + y = 7
$\Rightarrow$ x + 8 - z = 7
$\Rightarrow$ 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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