ma78s

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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romsek

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

$A = \pi R^2 = \pi r^2(1+\sqrt{2})^2 = \pi r (3+2\sqrt{2})$

$A = (3+2\sqrt{3})\pi (5.2) = 30.3078 \pi$