Circles

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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
Convert $225^\circ$ to radians. Give the exact value.
Convert $\pi$ radians to degrees.
A circle has radius 4 cm. What is the length of the arc cut off by a central angle of $\frac{3 \pi}{4}$ ? Give the exact value, in cm.

Answers

$\frac{49}{2}$
$90$
$23$
$8$
$119$
$90^\circ$
$52$
A rectangle (for example 9 by 11)
$67$
$\frac{304 \pi}{45}$
$\frac{235 \pi}{18}$
$6 \pi$
$\frac{5 \pi}{4}$
$180$
$3 \pi$