Circles Unit Test Flashcards

Questions and Answers

A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute. Approximately how far will a passenger travel during a 5-minute ride?

3,956 feet

659 feet

1,978 feet (correct)

132 feet

Line segment ON is perpendicular to line segment ML. What is the length of segment NP?

2 units (correct)

4 units

3 units

1 unit

In circle P, diameter QS measures 20 centimeters. What is the approximate length of arc QR? Round to the nearest tenth of a centimeter.

21.5 centimeters

43.0 centimeters

9.9 centimeters (correct)

19.9 centimeters

What is the measure of arc BEC in circle D?

134° Signup and view all the answers

What is the measure of arc QR?

104° Signup and view all the answers

In the diagram of circle A, what is the measure of ∠XYZ?

35° Signup and view all the answers

Which equation represents the circle described? The radius is 2 units. The center is the same as the center of a circle whose equation is x² + y² - 8x - 6y + 24 = 0.

(x - 4)² + (y - 3)² = 2² Signup and view all the answers

Angle BCD is a circumscribed angle of circle A. Angle BAC measures 53°. What is the measure of angle BCD?

74° Signup and view all the answers

A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0). What is the equation of the directrix of the parabola?

x = -3 Signup and view all the answers

In circle O, what is m∠MAJ?

55° Signup and view all the answers

In circle C, r = 32 units. What is the area of circle C?

1024π units² Signup and view all the answers

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis. Which could be the equation of the parabola?

x² = 4y Signup and view all the answers

Line segment KL is tangent to circle J at point K. What is the length of the radius, r?

10 units Signup and view all the answers

What is the area of the sector that is not shaded?

120π units² Signup and view all the answers

In circle O, AD and BE are diameters. The measure of arc AB is 55° and the measure of arc CD is 25°. What is the measure of EAC?

280° Signup and view all the answers

What is the radius of a circle whose equation is (x + 5)² + (y - 3)² = 42?

4 units Signup and view all the answers

Which is true regarding secants and chords?

Chords and secants intersect the perimeter of a circle twice. Chords are segments entirely within a circle, while secants are lines or rays that extend through a circle. Signup and view all the answers

What is the value of x?

2 Signup and view all the answers

What is the length of JG?

5 units Signup and view all the answers

Line segments XY and ZY are tangent to circle O. Which kind of triangle must triangle XYZ be?

An isosceles triangle Signup and view all the answers

Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment GX. Marco wants to create a new circle using GX as a radius. What will be the area of Marco's new circle?

676π cm² Signup and view all the answers

In the diagram of circle A, what is m∠LMN?

90° Signup and view all the answers

A general formula for a parabola is x²=4py. What is the value of p in the equation x²=12y?

p=3 Signup and view all the answers

A parabola can be represented by the equation x² = 2y. What are the coordinates of the focus and the equation of the directrix?

focus: [0, 1/2]; directrix: y = -1/2 Signup and view all the answers

Consider a circle whose equation is x² + y² - 2x - 8 = 0. Which statements are true? Select three options.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. Signup and view all the answers

Study Notes

Circle Measurements and Properties

A Ferris wheel with a 42-foot diameter travels approximately 1,978 feet in a 5-minute ride at 3 rotations per minute.
In circle P, the length of arc QR is approximately 9.9 centimeters when diameter QS measures 20 centimeters.
The measure of arc BEC in circle D is 134°, while arc QR measures 104°.
Angle XYZ in circle A measures 35°, and angle BCD (circumscribed angle) is 74° given angle BAC is 53°.

Circle Equations and Attributes

The equation of a circle with radius 2 units centered at (4, 3) is (x - 4)² + (y - 3)² = 2².
A circle with equation (x + 5)² + (y - 3)² = 42 has a radius of 4 units.
The area of circle C with radius 32 units is 1024π units².

Parabolas and Their Components

A parabola with vertex at (0, 0) and directrix on the negative y-axis is represented by x² = 4y.
For the equation x² = 12y, the value of p is 3; the coordinates of the focus are [0, 1/2] and the directrix is y = -1/2.

Tangents, Chords, and Angles

Line segment KL is tangent to circle J, with a radius of 10 units at the point of tangency.
Chords intersect the circle at two points, while secants extend through the circle.

Triangle XYZ, formed by tangent segments from point Y to circle O, is an isosceles triangle.
In a circle where diameters AD and BE intersect, the measure of angle EAC is 280° based on arc measures.

Sector and Area Calculations

The area of the non-shaded sector of a circle is 120π units².
Marco's new circle, using radius defined by line segment GX, has an area of 676π cm².

Additional Measurements and Insights

Line segments XY and ZY, tangent to circle O, form an isosceles triangle with equal tangent lengths.
Length and angle measurements within circles can greatly affect the calculations for areas, perimeters, and angles associated with different geometric figures.

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Description

Test your knowledge of circles with this engaging flashcard quiz. Each card presents a problem related to the properties and measurement of circles. Challenge yourself and see how many you can answer correctly!