SAT: Geometry & Trig - Circles - Matt Wheeland | Library

1

A circle in the $xy$-plane has the equation $(x - 13)^2 + (y - k)^2 = 64$. Which of the following gives the center of the circle and its radius?

The center is at $(13, k)$ and the radius is 8.

The center is at $(k, 13)$ and the radius is 8.

The center is at $(k, 13)$ and the radius is 64.

The center is at $(13, k)$ and the radius is 64.

1

The equation $(x + 6)^2 + (y + 3)^2 = 121$ defines a circle in the $xy$-plane. What is the radius of the circle?

1

Point $O$ is the center of a circle. The measure of arc $\overset{\frown}{RS}$ on this circle is $100^\circ$. What is the measure, in degrees, of its associated angle $\angle ROS$?

1

What is the diameter of the circle in the $xy$-plane with equation $(x - 5)^2 + (y - 3)^2 = 16$?

4

8

16

32

1

Circle A in the $xy$-plane has the equation $(x + 5)^2 + (y - 5)^2 = 4$. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the $xy$-plane is $(x + 5)^2 + (y - 5)^2 = k$, where $k$ is a constant. What is the value of $k$?

1

A circle in the $xy$-plane has a diameter with endpoints $(2, 4)$ and $(2, 14)$. An equation of this circle is $(x - 2)^2 + (y - 9)^2 = r^2$, where $r$ is a positive constant. What is the value of $r$?

1

Point $O$ is the center of the circle above, and the measure of $\angle OAB$ is $30^\circ$. If the length of $\overline{OC}$ is $18$, what is the length of arc $\widehat{AB}$?

$9\pi$

$12\pi$

$15\pi$

$18\pi$

1

$x^2 + 20x + y^2 + 16y = -20$
The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

$(-20,-16)$

$(-10,-8)$

$(10,8)$

$(20,16)$

1

$(x + 4)^2 + (y - 19)^2 = 121$
The graph of the given equation is a circle in the $xy$-plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a$?

$-16$

$-14$

$11$

$19$

1

Point $F$ lies on a unit circle in the $xy$-plane and has coordinates $(1,0)$. Point $G$ is the center of the circle and has coordinates $(0,0)$. Point $H$ also lies on the circle and has coordinates $(-1,y)$, where $y$ is a constant. Which of the following could be the positive measure of angle $\angle FGH$, in radians?

$\dfrac{27\pi}{2}$

$\dfrac{29\pi}{2}$

$24\pi$

$25\pi$

1

The graph of $x^2 + x + y^2 + y = \frac{199}{2}$ in the $xy$-plane is a circle. What is the length of the circle’s radius?

1

The circle above has center $O$, the length of arc is , and . What is the length of arc ?

13π

18π

13/2 π

1

Points $Q$ and $R$ lie on a circle with center $P$. The radius of this circle is $9$ inches. Triangle $PQR$ has a perimeter of $31$ inches. What is the length, in inches, of $QR$?

$13\sqrt{2}$

$13$

$9\sqrt{2}$

$9$

1

A circle in the $xy$-plane has its center at $(-1,1)$. Line $t$ is tangent to this circle at the point $(5,-4)$. Which of the following points also lies on line $t$?

$\left(0,\frac{6}{5}\right)$

$(4,7)$

$(10,2)$

$(11,1)$

1

In the $xy$-plane, the graph of the equation $(x - 3)^2 + (y - 5)^2 = 9$ is a circle. The point $(6, c)$, where $c$ is a constant, lies on this circle. What is the value of $c$?

1

What is the value of $\sin 42\pi$?

0

$\dfrac{1}{2}$

$\dfrac{\sqrt{2}}{2}$

1

$x^2 + 14x + y^2 = 6y + 109$
In the $xy$-plane, the graph of the given equation is a circle. What is the length of the circle's radius?

$\sqrt{109}$

$\sqrt{149}$

$\sqrt{167}$

$\sqrt{341}$

1

A circle in the $xy$-plane has its center at $(-4,5)$ and the point $(-8,8)$ lies on the circle. Which equation represents this circle?

$(x-4)^2 + (y+5)^2 = 5$

$(x+4)^2 + (y-5)^2 = 5$

$(x-4)^2 + (y+5)^2 = 25$

$(x+4)^2 + (y-5)^2 = 25$

1

A circle in the xy-plane has equation $(x + 3)^2 + (y - 1)^2 = 25$. Which of the following points does NOT lie in the interior of the circle?

$(-7, 3)$

$(-3, 1)$

$(0, 0)$

$(3, 2)$

1

Circle A (shown) is defined by the equation $(x + 2)^2 + y^2 = 9$. Circle B (not shown) is the result of shifting circle A down 6 units and increasing the radius so that the radius of circle B is 2 times the radius of circle A. Which equation defines circle B?

$(x + 2)^2 + (y + 6)^2 = (4)(9)$

$2(x + 2)^2 + 2(y + 6)^2 = 9$

$(x + 2)^2 + (y - 6)^2 = (4)(9)$

$2(x + 2)^2 + 2(y - 6)^2 = 9$

1

Points $A$ and $B$ lie on a circle with radius $1$, and arc $\overarc{AB}$ has length $\frac{\pi}{3}$. What fraction of the circumference of the circle is the length of arc $\overarc{AB}$?

1

Note: Figure not drawn to scale.
The circle shown has center $O$, circumference $144\pi$, and diameters $\overline{PR}$ and $\overline{QS}$. The length of arc $PS$ is twice the length of arc $PQ$. What is the length of arc $QR$?

$24\pi$

$48\pi$

$72\pi$

$96\pi$

1

In the xy-plane above, points $P$, $Q$, $R$, and $T$ lie on the circle with center $O$. The degree measures of angles $\angle POQ$ and $\angle ROT$ are each $30^\circ$. What is the radian measure of angle $\angle QOR$?

$\dfrac{5}{6}\pi$

$\dfrac{3}{4}\pi$

$\dfrac{2}{3}\pi$

$\dfrac{1}{3}\pi$

1

The equation $x^2 + (y - 2)^2 = 36$ represents circle A. Circle B is obtained by shifting circle A down 4 units in the $xy$-plane. Which of the following equations represents circle B?

$x^2 + (y + 2)^2 = 36$

$x^2 + (y - 6)^2 = 36$

$(x - 4)^2 + (y - 2)^2 = 36$

$(x + 4)^2 + (y - 2)^2 = 36$

1

$(x - 6)^2 + (y - 3)^2 = 81$
The graph of the given equation in the $xy$-plane is a circle. What is the length of the radius of this circle?

3

6

9

81

1

In the xy-plane, a circle has center $C$ with coordinates $(h, k)$. Points $A$ and $B$ lie on the circle. Point $A$ has coordinates $\left(h + 1, k + \sqrt{102}\right)$, and $\angle ACB$ is a right angle. What is the length of $\overline{AB}$?

$\sqrt{206}$

$2\sqrt{102}$

$103\sqrt{2}$

$103\sqrt{3}$

1

A circle in the xy-plane has its center at $(-5, 2)$ and has a radius of $9$. An equation of this circle is $x^2 + y^2 + ax + by + c = 0$, where $a$, $b$, and $c$ are constants. What is the value of $c$?

1

$(x - 6)^2 + (y + 5)^2 = 16$
In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates $(10, -5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point Q?

$(2, -5)$

$(6, -1)$

$(6, -5)$

$(6, -9)$

1

Question: Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point?

$(x - 8)^2 + (y - 8)^2 = 16$

$(x - 8)^2 + (y - 4)^2 = 16$

$(x - 4)^2 + (y - 9)^2 = 16$

$x^2 + (y - 9)^2 = 16$

1

In the $xy$-plane, a circle with radius $5$ has center $(-8, 6)$. Which of the following is an equation of the circle?

$(x - 8)^2 + (y + 6)^2 = 25$

$(x + 8)^2 + (y - 6)^2 = 25$

$(x - 8)^2 + (y + 6)^2 = 5$

$(x + 8)^2 + (y - 6)^2 = 5$

1

A circle has center $O$, and points $A$ and $B$ lie on the circle. The measure of arc $AB$ is $45^\circ$ and the length of arc $AB$ is 3 inches. What is the circumference, in inches, of the circle?

3

6

9

24

1

A circle has center $G$, and points $M$ and $N$ lie on the circle. Line segments $MH$ and $NH$ are tangent to the circle at points $M$ and $N$, respectively. If the radius of the circle is $168$ millimeters and the perimeter of quadrilateral $GMHN$ is $3{,}856$ millimeters, what is the distance, in millimeters, between points $G$ and $H$?

$168$

$1{,}752$

$1{,}760$

$1{,}768$

1

What is the value of $\tan \dfrac{92\pi}{3}$?

$-\sqrt{3}$

$-\dfrac{\sqrt{3}}{3}$

$\dfrac{\sqrt{3}}{3}$

$\sqrt{3}$

1

The equation $x^2 + (y - 1)^2 = 49$ represents circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the following equations represents circle B?

$(x - 2)^2 + (y - 1)^2 = 49$

$x^2 + (y - 3)^2 = 49$

$(x + 2)^2 + (y - 1)^2 = 49$

$x^2 + (y + 1)^2 = 49$

1

The measure of angle $Z$ is $60^\circ$. What is the measure, in radians, of angle $Z$?

$\frac{1}{6}\pi$

$\frac{1}{3}\pi$

$\frac{2}{3}\pi$

$1\pi$

1

The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

75

120

195

390

1

The circle above with center O has a circumference of 36. What is the length of minor arc $\widehat{AC}$?

9

12

18

36

1

Circle A shown is defined by the equation $x^{2} + (y - 6)^{2} = 7$. Circle B (not shown) has the same radius but is translated 96 units to the right. If the equation of circle B is $(x - h)^{2} + (y - k)^{2} = a$, where $h$, $k$, and $a$ are constants, what is the value of $4a$?

1

ID: a0cacec1
An angle has a measure of $\frac{16\pi}{15}$ radians. What is the measure of the angle, in degrees?

1

$x^{2} + 58x + y^{2} = 0$
In the xy-plane, the graph of the given equation is a circle. What are the coordinates $(x, y)$ of the center of the circle?

$(0, 29)$

$(0, -29)$

$(29, 0)$

$(-29, 0)$

1

An angle has a measure of $\frac{9\pi}{20}$ radians. What is the measure of the angle in degrees?

1

A circle in the xy-plane has its center at $(16,17)$ and has a radius of $7k$. Which equation represents this circle?

$(x-16)^2+(y-17)^2=49k$

$(x-16)^2+(y-17)^2=49k^2$

$(x-16)^2+(y-17)^2=7k$

$(x-16)^2+(y-17)^2=7k^2$

1

Question: What is the center of the circle in the $xy$-plane defined by the equation $(x - 1)^2 + (y + 7)^2 = 1$?

$(-1, -7)$

$(-1, 7)$

$(1, -7)$

$(1, 7)$

1

In the xy-plane, the graph of $2x^2 - 6x + 2y^2 + 2y = 45$ is a circle. What is the radius of the circle?

5

6.5

$\sqrt{40}$

$\sqrt{50}$

1

A circle has center $O$, and points $R$ and $S$ lie on the circle. In triangle $ORS$, the measure of $\angle ROS$ is $88^\circ$. What is the measure of $\angle RSO$, in degrees? (Disregard the degree symbol when entering your answer.)

1

Points $M$, $N$, and $P$ lie on the circle shown. On this circle, minor arc $MN$ has a length of 39 centimeters and major arc $MPN$ has a length of 195 centimeters. What is the circumference, in centimeters, of the circle shown?

39

156

195

234

1

Which point lies on the circle whose equation is $(x - 6)^2 + (y + 5)^2 = 16$?

$(10, -5)$

$(1, 0)$

$(2, -5)$

$(6, -1)$

1

The number of radians in a 720-degree angle can be written as $a\pi$, where $a$ is a constant. What is the value of $a$?

1

Circle A has equation $(x - 7)^2 + (y + 3)^2 = 1$. In the $xy$-plane, circle B is obtained by translating circle A to the right 4 units. Which equation represents circle B?

$(x - 7)^2 + (y + 7)^2 = 1$

$(x - 3)^2 + (y + 3)^2 = 1$

$(x - 11)^2 + (y + 3)^2 = 1$

$(x - 7)^2 + (y - 1)^2 = 1$

1

A circle in the $xy$-plane has its center at $(-4,-6)$. Line $k$ is tangent to this circle at the point $(-7,-7)$. What is the slope of line $k$?

$-3$

$-\dfrac{1}{3}$

$\dfrac{1}{3}$

$3$

SAT: Geometry & Trig - Circles

SAT: Geometry & Trig - Circles

A circle in the $xy$-plane has the equation $(x - 13)^2 + (y - k)^2 = 64$. Which of the following gives the center of the circle and its radius?

The equation $(x + 6)^2 + (y + 3)^2 = 121$ defines a circle in the $xy$-plane. What is the radius of the circle?

Point $O$ is the center of a circle. The measure of arc $\overset{\frown}{RS}$ on this circle is $100^\circ$. What is the measure, in degrees, of its associated angle $\angle ROS$?

What is the diameter of the circle in the $xy$-plane with equation $(x - 5)^2 + (y - 3)^2 = 16$?

A circle in the $xy$-plane has a diameter with endpoints $(2, 4)$ and $(2, 14)$. An equation of this circle is $(x - 2)^2 + (y - 9)^2 = r^2$, where $r$ is a positive constant. What is the value of $r$?

Point $O$ is the center of the circle above, and the measure of $\angle OAB$ is $30^\circ$. If the length of $\overline{OC}$ is $18$, what is the length of arc $\widehat{AB}$?

$x^2 + 20x + y^2 + 16y = -20$The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

$(x + 4)^2 + (y - 19)^2 = 121$The graph of the given equation is a circle in the $xy$-plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a$?

The graph of $x^2 + x + y^2 + y = \frac{199}{2}$ in the $xy$-plane is a circle. What is the length of the circle’s radius?

The circle above has center $O$, the length of arc is , and . What is the length of arc ?

Points $Q$ and $R$ lie on a circle with center $P$. The radius of this circle is $9$ inches. Triangle $PQR$ has a perimeter of $31$ inches. What is the length, in inches, of $QR$?

A circle in the $xy$-plane has its center at $(-1,1)$. Line $t$ is tangent to this circle at the point $(5,-4)$. Which of the following points also lies on line $t$?

In the $xy$-plane, the graph of the equation $(x - 3)^2 + (y - 5)^2 = 9$ is a circle. The point $(6, c)$, where $c$ is a constant, lies on this circle. What is the value of $c$?

What is the value of $\sin 42\pi$?

$x^2 + 14x + y^2 = 6y + 109$In the $xy$-plane, the graph of the given equation is a circle. What is the length of the circle's radius?

A circle in the $xy$-plane has its center at $(-4,5)$ and the point $(-8,8)$ lies on the circle. Which equation represents this circle?

A circle in the xy-plane has equation $(x + 3)^2 + (y - 1)^2 = 25$. Which of the following points does NOT lie in the interior of the circle?

Circle A (shown) is defined by the equation $(x + 2)^2 + y^2 = 9$. Circle B (not shown) is the result of shifting circle A down 6 units and increasing the radius so that the radius of circle B is 2 times the radius of circle A. Which equation defines circle B?

Points $A$ and $B$ lie on a circle with radius $1$, and arc $\overarc{AB}$ has length $\frac{\pi}{3}$. What fraction of the circumference of the circle is the length of arc $\overarc{AB}$?

Note: Figure not drawn to scale.The circle shown has center $O$, circumference $144\pi$, and diameters $\overline{PR}$ and $\overline{QS}$. The length of arc $PS$ is twice the length of arc $PQ$. What is the length of arc $QR$?

In the xy-plane above, points $P$, $Q$, $R$, and $T$ lie on the circle with center $O$. The degree measures of angles $\angle POQ$ and $\angle ROT$ are each $30^\circ$. What is the radian measure of angle $\angle QOR$?

The equation $x^2 + (y - 2)^2 = 36$ represents circle A. Circle B is obtained by shifting circle A down 4 units in the $xy$-plane. Which of the following equations represents circle B?

$(x - 6)^2 + (y - 3)^2 = 81$The graph of the given equation in the $xy$-plane is a circle. What is the length of the radius of this circle?

In the xy-plane, a circle has center $C$ with coordinates $(h, k)$. Points $A$ and $B$ lie on the circle. Point $A$ has coordinates $\left(h + 1, k + \sqrt{102}\right)$, and $\angle ACB$ is a right angle. What is the length of $\overline{AB}$?

A circle in the xy-plane has its center at $(-5, 2)$ and has a radius of $9$. An equation of this circle is $x^2 + y^2 + ax + by + c = 0$, where $a$, $b$, and $c$ are constants. What is the value of $c$?

$(x - 6)^2 + (y + 5)^2 = 16$In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates $(10, -5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point Q?

Question: Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point?

In the $xy$-plane, a circle with radius $5$ has center $(-8, 6)$. Which of the following is an equation of the circle?

A circle has center $O$, and points $A$ and $B$ lie on the circle. The measure of arc $AB$ is $45^\circ$ and the length of arc $AB$ is 3 inches. What is the circumference, in inches, of the circle?

What is the value of $\tan \dfrac{92\pi}{3}$?

The equation $x^2 + (y - 1)^2 = 49$ represents circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the following equations represents circle B?

The measure of angle $Z$ is $60^\circ$. What is the measure, in radians, of angle $Z$?

The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

The circle above with center O has a circumference of 36. What is the length of minor arc $\widehat{AC}$?

Circle A shown is defined by the equation $x^{2} + (y - 6)^{2} = 7$. Circle B (not shown) has the same radius but is translated 96 units to the right. If the equation of circle B is $(x - h)^{2} + (y - k)^{2} = a$, where $h$, $k$, and $a$ are constants, what is the value of $4a$?

ID: a0cacec1An angle has a measure of $\frac{16\pi}{15}$ radians. What is the measure of the angle, in degrees?

$x^{2} + 58x + y^{2} = 0$In the xy-plane, the graph of the given equation is a circle. What are the coordinates $(x, y)$ of the center of the circle?

An angle has a measure of $\frac{9\pi}{20}$ radians. What is the measure of the angle in degrees?

A circle in the xy-plane has its center at $(16,17)$ and has a radius of $7k$. Which equation represents this circle?

Question: What is the center of the circle in the $xy$-plane defined by the equation $(x - 1)^2 + (y + 7)^2 = 1$?

In the xy-plane, the graph of $2x^2 - 6x + 2y^2 + 2y = 45$ is a circle. What is the radius of the circle?

A circle has center $O$, and points $R$ and $S$ lie on the circle. In triangle $ORS$, the measure of $\angle ROS$ is $88^\circ$. What is the measure of $\angle RSO$, in degrees? (Disregard the degree symbol when entering your answer.)

Points $M$, $N$, and $P$ lie on the circle shown. On this circle, minor arc $MN$ has a length of 39 centimeters and major arc $MPN$ has a length of 195 centimeters. What is the circumference, in centimeters, of the circle shown?

Which point lies on the circle whose equation is $(x - 6)^2 + (y + 5)^2 = 16$?

The number of radians in a 720-degree angle can be written as $a\pi$, where $a$ is a constant. What is the value of $a$?

Circle A has equation $(x - 7)^2 + (y + 3)^2 = 1$. In the $xy$-plane, circle B is obtained by translating circle A to the right 4 units. Which equation represents circle B?

A circle in the $xy$-plane has its center at $(-4,-6)$. Line $k$ is tangent to this circle at the point $(-7,-7)$. What is the slope of line $k$?

A circle in the $xy$-plane has the equation $(x - 13)^2 + (y - k)^2 = 64$. Which of the following gives the center of the circle and its radius?

The equation $(x + 6)^2 + (y + 3)^2 = 121$ defines a circle in the $xy$-plane. What is the radius of the circle?

Point $O$ is the center of a circle. The measure of arc $\overset{\frown}{RS}$ on this circle is $100^\circ$. What is the measure, in degrees, of its associated angle $\angle ROS$?

What is the diameter of the circle in the $xy$-plane with equation $(x - 5)^2 + (y - 3)^2 = 16$?

A circle in the $xy$-plane has a diameter with endpoints $(2, 4)$ and $(2, 14)$. An equation of this circle is $(x - 2)^2 + (y - 9)^2 = r^2$, where $r$ is a positive constant. What is the value of $r$?

Point $O$ is the center of the circle above, and the measure of $\angle OAB$ is $30^\circ$. If the length of $\overline{OC}$ is $18$, what is the length of arc $\widehat{AB}$?

$x^2 + 20x + y^2 + 16y = -20$The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

$(x + 4)^2 + (y - 19)^2 = 121$The graph of the given equation is a circle in the $xy$-plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a$?

The graph of $x^2 + x + y^2 + y = \frac{199}{2}$ in the $xy$-plane is a circle. What is the length of the circle’s radius?

The circle above has center $O$, the length of arc is , and . What is the length of arc ?

Points $Q$ and $R$ lie on a circle with center $P$. The radius of this circle is $9$ inches. Triangle $PQR$ has a perimeter of $31$ inches. What is the length, in inches, of $QR$?

A circle in the $xy$-plane has its center at $(-1,1)$. Line $t$ is tangent to this circle at the point $(5,-4)$. Which of the following points also lies on line $t$?

In the $xy$-plane, the graph of the equation $(x - 3)^2 + (y - 5)^2 = 9$ is a circle. The point $(6, c)$, where $c$ is a constant, lies on this circle. What is the value of $c$?

What is the value of $\sin 42\pi$?

$x^2 + 14x + y^2 = 6y + 109$In the $xy$-plane, the graph of the given equation is a circle. What is the length of the circle's radius?

A circle in the $xy$-plane has its center at $(-4,5)$ and the point $(-8,8)$ lies on the circle. Which equation represents this circle?

A circle in the xy-plane has equation $(x + 3)^2 + (y - 1)^2 = 25$. Which of the following points does NOT lie in the interior of the circle?

Circle A (shown) is defined by the equation $(x + 2)^2 + y^2 = 9$. Circle B (not shown) is the result of shifting circle A down 6 units and increasing the radius so that the radius of circle B is 2 times the radius of circle A. Which equation defines circle B?

Points $A$ and $B$ lie on a circle with radius $1$, and arc $\overarc{AB}$ has length $\frac{\pi}{3}$. What fraction of the circumference of the circle is the length of arc $\overarc{AB}$?

Note: Figure not drawn to scale.The circle shown has center $O$, circumference $144\pi$, and diameters $\overline{PR}$ and $\overline{QS}$. The length of arc $PS$ is twice the length of arc $PQ$. What is the length of arc $QR$?

In the xy-plane above, points $P$, $Q$, $R$, and $T$ lie on the circle with center $O$. The degree measures of angles $\angle POQ$ and $\angle ROT$ are each $30^\circ$. What is the radian measure of angle $\angle QOR$?

The equation $x^2 + (y - 2)^2 = 36$ represents circle A. Circle B is obtained by shifting circle A down 4 units in the $xy$-plane. Which of the following equations represents circle B?

$(x - 6)^2 + (y - 3)^2 = 81$The graph of the given equation in the $xy$-plane is a circle. What is the length of the radius of this circle?

In the xy-plane, a circle has center $C$ with coordinates $(h, k)$. Points $A$ and $B$ lie on the circle. Point $A$ has coordinates $\left(h + 1, k + \sqrt{102}\right)$, and $\angle ACB$ is a right angle. What is the length of $\overline{AB}$?

A circle in the xy-plane has its center at $(-5, 2)$ and has a radius of $9$. An equation of this circle is $x^2 + y^2 + ax + by + c = 0$, where $a$, $b$, and $c$ are constants. What is the value of $c$?

$(x - 6)^2 + (y + 5)^2 = 16$In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates $(10, -5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point Q?

Question: Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point?

In the $xy$-plane, a circle with radius $5$ has center $(-8, 6)$. Which of the following is an equation of the circle?

A circle has center $O$, and points $A$ and $B$ lie on the circle. The measure of arc $AB$ is $45^\circ$ and the length of arc $AB$ is 3 inches. What is the circumference, in inches, of the circle?

What is the value of $\tan \dfrac{92\pi}{3}$?

The equation $x^2 + (y - 1)^2 = 49$ represents circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the following equations represents circle B?

$x^2 + 20x + y^2 + 16y = -20$
The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

$(x + 4)^2 + (y - 19)^2 = 121$
The graph of the given equation is a circle in the $xy$-plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a$?

$x^2 + 14x + y^2 = 6y + 109$
In the $xy$-plane, the graph of the given equation is a circle. What is the length of the circle's radius?

Note: Figure not drawn to scale.
The circle shown has center $O$, circumference $144\pi$, and diameters $\overline{PR}$ and $\overline{QS}$. The length of arc $PS$ is twice the length of arc $PQ$. What is the length of arc $QR$?

$(x - 6)^2 + (y - 3)^2 = 81$
The graph of the given equation in the $xy$-plane is a circle. What is the length of the radius of this circle?

$(x - 6)^2 + (y + 5)^2 = 16$
In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates $(10, -5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point Q?

ID: a0cacec1
An angle has a measure of $\frac{16\pi}{15}$ radians. What is the measure of the angle, in degrees?

$x^{2} + 58x + y^{2} = 0$
In the xy-plane, the graph of the given equation is a circle. What are the coordinates $(x, y)$ of the center of the circle?

$x^2 + 20x + y^2 + 16y = -20$
The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

$(x + 4)^2 + (y - 19)^2 = 121$
The graph of the given equation is a circle in the $xy$-plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a$?

$x^2 + 14x + y^2 = 6y + 109$
In the $xy$-plane, the graph of the given equation is a circle. What is the length of the circle's radius?

Note: Figure not drawn to scale.
The circle shown has center $O$, circumference $144\pi$, and diameters $\overline{PR}$ and $\overline{QS}$. The length of arc $PS$ is twice the length of arc $PQ$. What is the length of arc $QR$?

$(x - 6)^2 + (y - 3)^2 = 81$
The graph of the given equation in the $xy$-plane is a circle. What is the length of the radius of this circle?

$(x - 6)^2 + (y + 5)^2 = 16$
In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates $(10, -5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point Q?

ID: a0cacec1
An angle has a measure of $\frac{16\pi}{15}$ radians. What is the measure of the angle, in degrees?

$x^{2} + 58x + y^{2} = 0$
In the xy-plane, the graph of the given equation is a circle. What are the coordinates $(x, y)$ of the center of the circle?