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Geometry and Measurement

SAT Composite Figures

         

\(\)

If \(m=14\) and \(\overline{XY}\) is a diameter in circle \(B,\) which of the following equals the area of circle \(A\) minus the area of circle \(B.\)

(A) \(\ \ 49 \pi\)
(B) \(\ \ 98\pi\)
(C) \(\ \ 147\pi\)
(D) \(\ \ 196\pi\)
(E) \(\ \ 294\pi\)

\(\)

If \(a=4\) in the cube above, what is the length of diagonal \(\overline{AB}?\)

(A) \(\ \ 4\)
(B) \(\ \ 4\sqrt{2}\)
(C) \(\ \ 4 \sqrt{3}\)
(D) \(\ \ 8\)
(E) \(\ \ 48\)

\(\)

Square \(ABCD\) is circumscribed about circle \(O.\) If the radius of the circle is \(5,\) what is the area of the square?

(A) \(\ \ 10\)
(B) \(\ \ 10\pi\)
(C) \(\ \ 25\)
(D) \(\ \ 25\pi\)
(E) \(\ \ 100\)

\(\)

In the figure above, circles \(A\) and \(C\) are tangent to each other at point \(B.\) If \(a=6\) and the \(b=10,\) what is the the length of segment \(\overline{DE}?\)

(A) \(\ \ 4\)
(B) \(\ \ \sqrt{60}\)
(C) \(\ \ \sqrt{240}\)
(D) \(\ \ 16\)
(E) \(\ \ 20\)

\(\)

In the figure above, \(AB\) is a diameter in \(\bigodot O\) and \(\overline{DC} \parallel \overline{AB}.\) If \(\angle DOC = 60^\circ,\) and the area of \(\triangle DOC\) equals \(\frac{121\sqrt{3}}{4},\) what is the area of \(\triangle ABC?\)

(A) \(\ \ \frac{121\sqrt{3}}{4}\)

(B) \(\ \ \frac{121\sqrt{3}}{2}\)

(C) \(\ \ 121\)

(D) \(\ \ \frac{363\sqrt{3}}{4}\)

(E) \(\ \ \frac{121\pi}{2}\)

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