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# SAT Circles



If the radius of $$\bigodot O$$ is $$18,$$ what is the area of the shaded region?

(A) $$\ \ 81\pi - 162$$
(B) $$\ \ 162$$
(C) $$\ \ 81 \pi$$
(D) $$\ \ 324\pi - 162$$
(E) $$\ \ 324\pi$$

The circles above are tangent to each other. If the circles are congruent, and the radius of one circle is $$2,$$ what is the perimeter of the polygon formed when connecting their centers?

(A) $$\ \ 4$$
(B) $$\ \ 16$$
(C) $$\ \ 28$$
(D) $$\ \ 32$$
(E) $$\ \ 36$$



If the area of $$\triangle ABC$$ is $$24$$ and the area of $$\bigodot A$$ is $$144\pi,$$ what is the length of $$\overline{CD}?$$

(A) $$\ \ 2$$
(B) $$\ \ 4$$
(C) $$\ \ 12$$
(D) $$\ \ 48$$
(E) $$\ \ 144$$

In the rectangle above, the four congruent semicircles are tangent to each other. If the length of the rectangle is $$24,$$ what is the area of the shaded region?

(A) $$\ \ 288 - 72 \pi$$
(B) $$\ \ 288 - 36\pi$$
(C) $$\ \ 72\pi$$
(D) $$\ \ 192 - 288\pi$$
(E) $$\ \ 216\pi$$



$$\overline{DA}$$ is a diameter in $$\bigodot O$$ above and $$\overline{AB} \parallel \overline{OC}.$$ If $$m\angle OAB=25^\circ,$$ what is the ratio $$m\widehat{DC} : m\widehat{CB}?$$

(A) $$\ \ 1:1$$
(B) $$\ \ 1:2$$
(C) $$\ \ 1:3$$
(D) $$\ \ 2:1$$
(E) $$\ \ 2:3$$

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