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

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 equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

Point O is the center of the circle above, and the measure of is . If the length of is 18, what is the length of arc ?

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

Circle A in the xy-plane has the equation ${\left(x+5\right)}^2+{\left(y-5\right)}^2=4$. 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 ${\left(x+5\right)}^2+{\left(y-5\right)}^2=k$, where $k$ is a constant. What is the value of $k$?

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

Point $O$ is the center of a circle. The measure of arc $RS$ on this circle is $100°$. What is the measure, in degrees, of its associated angle $ROS$?

The equation defines a circle in the xy‑plane. What is the radius of the circle?

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

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

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

In the xy-plane, the graph of is a circle. What is the radius of the circle?

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

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

The circle above with center O has a circumference of 36. What is the length of minor arc ?

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 equation $x^2+{\left(y-1\right)}^2=49$ 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?

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?

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

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, the graph of the equation above is a circle. Point P is on the circle and has coordinates . If is a diameter of the circle, what are the coordinates of point Q ?

A circle in the xy-plane has its center at $\left(-5,2\right)$ 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 $c$?

The equation $x^2+{\left(y-2\right)}^2=36$ 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?

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