My Math Forum Area of circle

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March 20th, 2017, 11:42 PM   #1
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Area of circle

Does anybody know how to find the area of the larger circle knowing only that the radius of the smaller inner circles is equal to 5.2 ? thanks in advance,
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 March 21st, 2017, 12:55 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314 draw a square connecting the centers of the smaller circles. It has side length $2r$ It's diagonal has length $d = 2\sqrt{2}r$ The diameter of the larger circle is $D = 2r + d = 2r(1+\sqrt{2})$ and it's radius $R = r(1+\sqrt{2})$ with area $A = \pi R^2 = \pi r^2(1+\sqrt{2})^2 = \pi r (3+2\sqrt{2})$ $A = (3+2\sqrt{3})\pi (5.2) = 30.3078 \pi$ Thanks from topsquark

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