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Geometry and Measurement

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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