1.
AB is a diameter of the circle.
| Quantity A | Quantity B |
| The length of \(\)AB\(\) | The average (arithmetic mean) of the lengths of \(\)AC\(\) and \(\)AD\(\) |
2. In the figure above, \(\)O\(\) and \(\)P\(\) are the centers of the two circles. If each circle has radius \(\)r\(\), what is the area of the shaded region?
(A) \(\)\frac { \sqrt { 2 } }{ 2 } { r }^{ 2 }\(\)
(B) \(\)\frac { \sqrt { 3 } }{ 2 } { r }^{ 2 }\(\)
(C) \(\)\sqrt { 2 } { r }^{ 2 }\(\)
(D) \(\)\sqrt { 3 } { r }^{ 2 }\(\)
(E) \(\)2\sqrt { 3 } { r }^{ 2 }\(\)
3.
| Quantity A | Quantity B |
| The greatest possible number of points common to a triangle and a circle | \(\)3\(\) |
4. In the figure, \(\)O\(\) is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?
(A) Always less than \(\)10\(\)
(B) Always greater than \(\)40\(\)
(C) Always greater than \(\)30\(\)
(D) Always less than \(\)30\(\)
(E) Less than \(\)40\(\) and greater than \(\)20\(\)
5. In the figure, \(\)P\(\) and \(\)Q\(\) are centers of the two circles of radius \(\)3\(\) and \(\)4\(\), respectively. \(\)A\(\) and \(\)B\(\) are the points at which a common tangent touches each circle.
| Quantity A | Quantity B |
| \(\)AB\(\) | \(\)PQ\(\) |
6. In the, figure \(\)A, B\(\) and \(\)C\(\) are points on the circle. What is the value of \(\)x\(\) ?
(A) \(\)45\(\)
(B) \(\)55\(\)
(C) \(\)60\(\)
(D) \(\)65\(\)
(E) \(\)70\(\)
7. \(\)AB\(\) and \(\)CD\(\) are chords of the circle, and \(\)E\(\) and \(\)F\(\) are the midpoints of the chords, respectively. The line \(\)EF\(\) passes through the center \(\)O\(\) of the circle. If \(\)EF = 17\(\), then what is radius of the circle?
(A) \(\)10\(\)
(B) \(\)12\(\)
(C) \(\)13\(\)
(D) \(\)15\(\)
(E) \(\)25\(\)
8. A sector of a circle has an arc length of \(\)7\(\)π. If the diameter of the circle is \(\)14\(\), what is the measure of the central angle of the sector, in degrees?
(A) \(\)45\(\)
(B) \(\)60\(\)
(C) \(\)90\(\)
(D) \(\)120\(\)
(E) \(\)180\(\)
9. If a solid right circular cylinder with height \(\)9\(\) and radius \(\)2\(\) is cut as shown into three new cylinders, each of equal and uniform height, how much new surface area is created?
(A) \(\)4\(\)π
(B) \(\)12\(\)π
(C) \(\)16\(\)π
(D) \(\)24\(\)π
(E) \(\)36\(\)π
10.
Point O is the center of the circle above.
| Quantity A | Quantity B |
| The ratio of the length of minor arc \(\)AB\(\) to major arc \(\)AB\(\) | \(\)\frac { 1 }{ 6 }\(\) |
11. The radius of circle A is 12 greater than the radius of circle B.
| Quantity A | Quantity B |
| The circumference of circle \(\)A\(\) minus circumference of circle \(\)B\(\) | \(\)72\(\) |
12. A circle is inscribed in a square with sides of length \(\)5\(\).
| Quantity A | Quantity B |
| The circumference of the circle |
\(\)15\(\) |
13.
In the figure above, the diameter of the circle is 10.
| Quantity A | Quantity B |
| The area of quadrilateral \(\)ABCD\(\) |
\(\)40\(\) |
14. The relationship between the area A of a circle and its circumference \(\)C\(\) is given by the formula \(\)A=k{ C }^{ 2 }\(\), where \(\)k\(\) is a constant. What is the value of \(\)k\(\) ?
(A) \(\)\frac { 1 }{ 4\pi }\(\)
(B) \(\)\frac { 1 }{ 2\pi }\(\)
(C) \(\)\frac { 1 }{ 4 }\(\)
(D) \(\)2\(\)π
(E) \(\)2{ \pi }^{ 2 }\(\)
15. The circle with center \(\)O\(\) below has radius \(\)4\(\). Find the following.
(a) Circumference of the circle
(b) Length of arc \(\)ABC\(\)
(c) Area of the shaded region
Answers:
1 C: The two quantities are equal.
2 B
3 A
4 E
5 B
6 B
7 C
8 E
9 C
10 A
11 A
12 C
13 D
14 A
15 (a) 8π (b) 8π/9 (c) 16π/9
