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A central angle measures $49^\circ$ . Find an inscribed angle that intercepts the same arc (degrees).
An inscribed angle measures $45^\circ$ . Find the central angle on the same arc (degrees).
Triangle $ABC$ is inscribed in a circle with $AB$ a diameter, and $\angle A = 67^\circ$ . Find $\angle B$ (degrees).
A circle has radius 6. Point $P$ is 10 from the center. Find the length of a tangent segment from $P$ to the circle.
Two tangents from $P$ touch a circle (center $O$ ) at $A$ and $B$ , with $\angle APB = 61^\circ$ . Find $\angle AOB$ (degrees).
A line touches a circle of radius 7 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 9 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 6 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 8 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 5 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 2 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 3 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
A line touches a circle of radius 4 at exactly one point $T$ . What is the angle between the line and the radius to $T$ ?
1. $90^\circ$
2. It depends on the radius
3. $0^\circ$ : they lie along each other
$ABCD$ is inscribed in a circle and $\angle A = 128^\circ$ . Find $\angle C$ (degrees).
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 9 by 11)
2. Any parallelogram
3. Any rhombus
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 4 by 6)
2. Any parallelogram
3. Any rhombus
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 6 by 8)
2. Any parallelogram
3. Any rhombus
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 8 by 10)
2. Any parallelogram
3. Any rhombus
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 7 by 9)
2. Any parallelogram
3. Any rhombus
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 3 by 5)
2. Any parallelogram
3. Any rhombus
Which quadrilateral can always be inscribed in a circle?
1. A rectangle (for example 5 by 7)
2. Any parallelogram
3. Any rhombus
$PQRS$ is inscribed in a circle with $\angle Q = 113^\circ$ . Find $\angle S$ (degrees).
A circle has radius 8 cm. Find the length of an arc with central angle $152^\circ$ (exact, in terms of π).Not to scale
Find the area of a sector with radius 5 cm and central angle $188^\circ$ (exact, in terms of π).Not to scale
Find the length of the arc cut off by a $90^\circ$ central angle in a circle of radius 12 (exact).Not to scale
What is the radius of the circle $(x - 9)^2 + (y + 1)^2 = 16$ ?
Which is the equation of the circle with center $(2, -8)$ and radius 7?
1. $(x - 2)^2 + (y + 8)^2 = 49$
2. $(x + 2)^2 + (y - 8)^2 = 49$
3. $(x - 2)^2 + (y + 8)^2 = 7$
Which is the equation of the circle with center $(7, -2)$ and radius 9?
1. $(x - 7)^2 + (y + 2)^2 = 81$
2. $(x + 7)^2 + (y - 2)^2 = 81$
3. $(x - 7)^2 + (y + 2)^2 = 9$
Which is the equation of the circle with center $(6, -1)$ and radius 6?
1. $(x - 6)^2 + (y + 1)^2 = 36$
2. $(x + 6)^2 + (y - 1)^2 = 36$
3. $(x - 6)^2 + (y + 1)^2 = 6$
Which is the equation of the circle with center $(6, -8)$ and radius 7?
1. $(x - 6)^2 + (y + 8)^2 = 49$
2. $(x + 6)^2 + (y - 8)^2 = 49$
3. $(x - 6)^2 + (y + 8)^2 = 7$
Which is the equation of the circle with center $(9, -8)$ and radius 4?
1. $(x - 9)^2 + (y + 8)^2 = 16$
2. $(x + 9)^2 + (y - 8)^2 = 16$
3. $(x - 9)^2 + (y + 8)^2 = 4$
Which is the equation of the circle with center $(1, -4)$ and radius 5?
1. $(x - 1)^2 + (y + 4)^2 = 25$
2. $(x + 1)^2 + (y - 4)^2 = 25$
3. $(x - 1)^2 + (y + 4)^2 = 5$
Which is the equation of the circle with center $(7, -5)$ and radius 5?
1. $(x - 7)^2 + (y + 5)^2 = 25$
2. $(x + 7)^2 + (y - 5)^2 = 25$
3. $(x - 7)^2 + (y + 5)^2 = 5$
Which is the equation of the circle with center $(9, -8)$ and radius 3?
1. $(x - 9)^2 + (y + 8)^2 = 9$
2. $(x + 9)^2 + (y - 8)^2 = 9$
3. $(x - 9)^2 + (y + 8)^2 = 3$
Which is the equation of the circle with center $(8, -2)$ and radius 6?
1. $(x - 8)^2 + (y + 2)^2 = 36$
2. $(x + 8)^2 + (y - 2)^2 = 36$
3. $(x - 8)^2 + (y + 2)^2 = 6$
Which is the equation of the circle with center $(3, -1)$ and radius 4?
1. $(x - 3)^2 + (y + 1)^2 = 16$
2. $(x + 3)^2 + (y - 1)^2 = 16$
3. $(x - 3)^2 + (y + 1)^2 = 4$
Which is the equation of the circle with center $(6, -5)$ and radius 4?
1. $(x - 6)^2 + (y + 5)^2 = 16$
2. $(x + 6)^2 + (y - 5)^2 = 16$
3. $(x - 6)^2 + (y + 5)^2 = 4$
Which is the equation of the circle with center $(5, -2)$ and radius 9?
1. $(x - 5)^2 + (y + 2)^2 = 81$
2. $(x + 5)^2 + (y - 2)^2 = 81$
3. $(x - 5)^2 + (y + 2)^2 = 9$
Which is the equation of the circle with center $(4, -5)$ and radius 4?
1. $(x - 4)^2 + (y + 5)^2 = 16$
2. $(x + 4)^2 + (y - 5)^2 = 16$
3. $(x - 4)^2 + (y + 5)^2 = 4$
Which is the equation of the circle with center $(7, -7)$ and radius 3?
1. $(x - 7)^2 + (y + 7)^2 = 9$
2. $(x + 7)^2 + (y - 7)^2 = 9$
3. $(x - 7)^2 + (y + 7)^2 = 3$
Which is the equation of the circle with center $(2, -5)$ and radius 6?
1. $(x - 2)^2 + (y + 5)^2 = 36$
2. $(x + 2)^2 + (y - 5)^2 = 36$
3. $(x - 2)^2 + (y + 5)^2 = 6$
Which is the equation of the circle with center $(9, -6)$ and radius 2?
1. $(x - 9)^2 + (y + 6)^2 = 4$
2. $(x + 9)^2 + (y - 6)^2 = 4$
3. $(x - 9)^2 + (y + 6)^2 = 2$
Which is the equation of the circle with center $(9, -6)$ and radius 6?
1. $(x - 9)^2 + (y + 6)^2 = 36$
2. $(x + 9)^2 + (y - 6)^2 = 36$
3. $(x - 9)^2 + (y + 6)^2 = 6$
Which is the equation of the circle with center $(7, -6)$ and radius 2?
1. $(x - 7)^2 + (y + 6)^2 = 4$
2. $(x + 7)^2 + (y - 6)^2 = 4$
3. $(x - 7)^2 + (y + 6)^2 = 2$
Which is the equation of the circle with center $(1, -9)$ and radius 9?
1. $(x - 1)^2 + (y + 9)^2 = 81$
2. $(x + 1)^2 + (y - 9)^2 = 81$
3. $(x - 1)^2 + (y + 9)^2 = 9$
Which is the equation of the circle with center $(8, -5)$ and radius 6?
1. $(x - 8)^2 + (y + 5)^2 = 36$
2. $(x + 8)^2 + (y - 5)^2 = 36$
3. $(x - 8)^2 + (y + 5)^2 = 6$
Which is the equation of the circle with center $(5, -6)$ and radius 5?
1. $(x - 5)^2 + (y + 6)^2 = 25$
2. $(x + 5)^2 + (y - 6)^2 = 25$
3. $(x - 5)^2 + (y + 6)^2 = 5$
Which is the equation of the circle with center $(6, -1)$ and radius 9?
1. $(x - 6)^2 + (y + 1)^2 = 81$
2. $(x + 6)^2 + (y - 1)^2 = 81$
3. $(x - 6)^2 + (y + 1)^2 = 9$
Which is the equation of the circle with center $(9, -2)$ and radius 9?
1. $(x - 9)^2 + (y + 2)^2 = 81$
2. $(x + 9)^2 + (y - 2)^2 = 81$
3. $(x - 9)^2 + (y + 2)^2 = 9$
Which is the equation of the circle with center $(9, -3)$ and radius 7?
1. $(x - 9)^2 + (y + 3)^2 = 49$
2. $(x + 9)^2 + (y - 3)^2 = 49$
3. $(x - 9)^2 + (y + 3)^2 = 7$
Which is the equation of the circle with center $(4, -8)$ and radius 9?
1. $(x - 4)^2 + (y + 8)^2 = 81$
2. $(x + 4)^2 + (y - 8)^2 = 81$
3. $(x - 4)^2 + (y + 8)^2 = 9$
Which is the equation of the circle with center $(1, -4)$ and radius 7?
1. $(x - 1)^2 + (y + 4)^2 = 49$
2. $(x + 1)^2 + (y - 4)^2 = 49$
3. $(x - 1)^2 + (y + 4)^2 = 7$
Which is the equation of the circle with center $(1, -7)$ and radius 4?
1. $(x - 1)^2 + (y + 7)^2 = 16$
2. $(x + 1)^2 + (y - 7)^2 = 16$
3. $(x - 1)^2 + (y + 7)^2 = 4$
Which is the equation of the circle with center $(8, -7)$ and radius 8?
1. $(x - 8)^2 + (y + 7)^2 = 64$
2. $(x + 8)^2 + (y - 7)^2 = 64$
3. $(x - 8)^2 + (y + 7)^2 = 8$
Which is the equation of the circle with center $(3, -2)$ and radius 5?
1. $(x - 3)^2 + (y + 2)^2 = 25$
2. $(x + 3)^2 + (y - 2)^2 = 25$
3. $(x - 3)^2 + (y + 2)^2 = 5$
Which is the equation of the circle with center $(1, -8)$ and radius 6?
1. $(x - 1)^2 + (y + 8)^2 = 36$
2. $(x + 1)^2 + (y - 8)^2 = 36$
3. $(x - 1)^2 + (y + 8)^2 = 6$
Which is the equation of the circle with center $(5, -7)$ and radius 7?
1. $(x - 5)^2 + (y + 7)^2 = 49$
2. $(x + 5)^2 + (y - 7)^2 = 49$
3. $(x - 5)^2 + (y + 7)^2 = 7$
Which is the equation of the circle with center $(8, -2)$ and radius 8?
1. $(x - 8)^2 + (y + 2)^2 = 64$
2. $(x + 8)^2 + (y - 2)^2 = 64$
3. $(x - 8)^2 + (y + 2)^2 = 8$
Which is the equation of the circle with center $(6, -5)$ and radius 6?
1. $(x - 6)^2 + (y + 5)^2 = 36$
2. $(x + 6)^2 + (y - 5)^2 = 36$
3. $(x - 6)^2 + (y + 5)^2 = 6$
Which is the equation of the circle with center $(9, -3)$ and radius 6?
1. $(x - 9)^2 + (y + 3)^2 = 36$
2. $(x + 9)^2 + (y - 3)^2 = 36$
3. $(x - 9)^2 + (y + 3)^2 = 6$
Which is the equation of the circle with center $(1, -1)$ and radius 6?
1. $(x - 1)^2 + (y + 1)^2 = 36$
2. $(x + 1)^2 + (y - 1)^2 = 36$
3. $(x - 1)^2 + (y + 1)^2 = 6$
Which is the equation of the circle with center $(3, -3)$ and radius 6?
1. $(x - 3)^2 + (y + 3)^2 = 36$
2. $(x + 3)^2 + (y - 3)^2 = 36$
3. $(x - 3)^2 + (y + 3)^2 = 6$
Which is the equation of the circle with center $(5, -2)$ and radius 6?
1. $(x - 5)^2 + (y + 2)^2 = 36$
2. $(x + 5)^2 + (y - 2)^2 = 36$
3. $(x - 5)^2 + (y + 2)^2 = 6$
Which is the equation of the circle with center $(3, -9)$ and radius 4?
1. $(x - 3)^2 + (y + 9)^2 = 16$
2. $(x + 3)^2 + (y - 9)^2 = 16$
3. $(x - 3)^2 + (y + 9)^2 = 4$
Which is the equation of the circle with center $(7, -9)$ and radius 2?
1. $(x - 7)^2 + (y + 9)^2 = 4$
2. $(x + 7)^2 + (y - 9)^2 = 4$
3. $(x - 7)^2 + (y + 9)^2 = 2$
Which is the equation of the circle with center $(1, -1)$ and radius 4?
1. $(x - 1)^2 + (y + 1)^2 = 16$
2. $(x + 1)^2 + (y - 1)^2 = 16$
3. $(x - 1)^2 + (y + 1)^2 = 4$
Which is the equation of the circle with center $(4, -7)$ and radius 3?
1. $(x - 4)^2 + (y + 7)^2 = 9$
2. $(x + 4)^2 + (y - 7)^2 = 9$
3. $(x - 4)^2 + (y + 7)^2 = 3$
Which is the equation of the circle with center $(9, -7)$ and radius 8?
1. $(x - 9)^2 + (y + 7)^2 = 64$
2. $(x + 9)^2 + (y - 7)^2 = 64$
3. $(x - 9)^2 + (y + 7)^2 = 8$
Which is the equation of the circle with center $(7, -2)$ and radius 8?
1. $(x - 7)^2 + (y + 2)^2 = 64$
2. $(x + 7)^2 + (y - 2)^2 = 64$
3. $(x - 7)^2 + (y + 2)^2 = 8$
Which is the equation of the circle with center $(2, -3)$ and radius 8?
1. $(x - 2)^2 + (y + 3)^2 = 64$
2. $(x + 2)^2 + (y - 3)^2 = 64$
3. $(x - 2)^2 + (y + 3)^2 = 8$
Which is the equation of the circle with center $(4, -4)$ and radius 5?
1. $(x - 4)^2 + (y + 4)^2 = 25$
2. $(x + 4)^2 + (y - 4)^2 = 25$
3. $(x - 4)^2 + (y + 4)^2 = 5$
Which is the equation of the circle with center $(4, -7)$ and radius 7?
1. $(x - 4)^2 + (y + 7)^2 = 49$
2. $(x + 4)^2 + (y - 7)^2 = 49$
3. $(x - 4)^2 + (y + 7)^2 = 7$
Which is the equation of the circle with center $(5, -9)$ and radius 4?
1. $(x - 5)^2 + (y + 9)^2 = 16$
2. $(x + 5)^2 + (y - 9)^2 = 16$
3. $(x - 5)^2 + (y + 9)^2 = 4$
Which is the equation of the circle with center $(4, -7)$ and radius 5?
1. $(x - 4)^2 + (y + 7)^2 = 25$
2. $(x + 4)^2 + (y - 7)^2 = 25$
3. $(x - 4)^2 + (y + 7)^2 = 5$
Which is the equation of the circle with center $(4, -8)$ and radius 8?
1. $(x - 4)^2 + (y + 8)^2 = 64$
2. $(x + 4)^2 + (y - 8)^2 = 64$
3. $(x - 4)^2 + (y + 8)^2 = 8$
Which is the equation of the circle with center $(6, -5)$ and radius 8?
1. $(x - 6)^2 + (y + 5)^2 = 64$
2. $(x + 6)^2 + (y - 5)^2 = 64$
3. $(x - 6)^2 + (y + 5)^2 = 8$
The parabola $x^2 = 8y$ has its focus at $(0, c)$ . What is $c$ ?
The parabola $y^2 = 8x$ has the directrix $x = d$ . What is $d$ ?
A parabola has focus $(0, 3)$ and directrix $y = -3$ . Its equation is $x^2 = ky$ . What is $k$ ?
Tap the point one third of the way from $A(-3, -2)$ to $B(3, 4)$ .
Point $P$ divides segment $AB$ in the ratio $1 : 2$ (closer to $A$ ). $A$ has $x = -4$ and $B$ has $x = 2$ . Find the $x$ -coordinate of $P$ .
Point $P$ divides $AB$ in the ratio $3 : 1$ from $A$ . $A$ has $x = -2$ , $B$ has $x = 1$ . Find $P$ 's $x$ -coordinate.

Answers

$\frac{49}{2}$
$90$
$23$
$8$
$119$
$90^\circ$
$52$
A rectangle (for example 9 by 11)
$67$
$\frac{304 \pi}{45}$
$\frac{235 \pi}{18}$
$6 \pi$
$4$
$(x - 2)^2 + (y + 8)^2 = 49$
$2$
$-2$
$12$
$(-1, 0)$
$-2$
$\frac{1}{4}$