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) \(\ \ 324\pi\)

(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) \(\ \ 144\)

(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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