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Two farmers have circular plots. The plots are watered with the same water source placed in the point Common to both the plots as shown in the figure. The sum of their areas is $130 π$ and the distance between their centres is $14 c m$ . What are the radii of the circles?

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An Intiative by Sri Chaitanya

12, 3 or 3, 12

11, 3 or 12, 3

11, 3 or 3, 11

11, 4 or 4, 12

answer is C.

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Detailed Solution

Given that the sum of the areas of the two plots is

130 π

and the distance between their centres is

14 c m

.
We have the following formulae,
Area of circle

= π r 2

We have the sum of areas,

⇒ 130 π

r 1 + r 2 = 14 cm

r 12 + 196 + r 12 − 28 r 1 = 130 2 r 12 − 28 r 1 + 60 = 0 r 12 − 14 r 1 + 33 = 0 r 12 − 11 r 1 − 3 r 1 + 33 = 0 r 1 = 3, 11

Thus the radii are 3, 11 or 11, 3.
Therefore the correct option is 3.

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