Seven Circles in Large One

The total area enclosed by the small circles is what fraction of the area enclosed by the larger circle?




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Suppose AB, the diameter of the large circle, is 30. Then the diameter of each small circle (e.g., AC) is 10.

The area of the small circles totals 7 · pi(5)2 = 175pi.
The area of the large circle is pi(15)2 = 225pi.

So we have  175pi  =  7 .
225pi 9

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