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(C) Let the radius of the smaller circle be $r_1 = 2$ and the radius of the larger circle be $r_2$.According to the problem,the area of the smaller ci

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$2$

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(C) Let the radius of the smaller circle be $r_1 = 2$ and the radius of the larger circle be $r_2$.According to the problem,the area of the smaller circle is equal to the area of the region between the two circles.$\pi r_1^2 = \pi r_2^2 - \pi r_1^2$$2 \pi r_1^2 = \pi r_2^2$$r_2^2 = 2 r_1^2$$r_2 = \sqrt{2} r_1 = 2\sqrt{2}$.Let $L$ be the length of the tangent from a point $P$ on the larger circle to the smaller circle.In the right-angled triangle formed by the radius of the smaller circle $(r_1)$,the tangent $(L)$,and the distance from the center to point $P$ $(r_2)$,we have:$L^2 + r_1^2 = r_2^2$$L^2 = r_2^2 - r_1^2$$L^2 = (2\sqrt{2})^2 - 2^2 = 8 - 4 = 4$$L = 2$.

Two concentric circles are such that the smaller divides the larger into two regions of equal area. If the radius of the smaller circle is $2$,then the length of the tangent from any point $P$ on the larger circle to the smaller circle is:

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