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