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 7π. 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) 4π
(B) 12π
(C) 16π
(D) 24π
(E) 36π

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) 2π
(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

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