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Circles: Definition, Characteristics, and Properties

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Circles: Definition, Characteristics, and Properties

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Questions and Answers

What is the definition of a circle?

A set of points in a plane that are closest to a fixed point

A set of points in a plane that are not equidistant from a fixed point

A set of points in a plane that are farthest from a fixed point

A set of points in a plane that are equidistant from a fixed point called the center (correct)

What is the longest distance across the circle, passing through the center?

Diameter (correct)

Radius

Circumference

Center

What is the formula to calculate the circumference of a circle?

C = 2 × π × radius (correct)

C = radius × radius

C = diameter × π

C = π × radius

What is the characteristic of a circle that makes it a closed curve?

<p>It has no beginning or end</p> Signup and view all the answers

What is the circumference of a semi-circle?

<p>Half the circumference of the original circle</p> Signup and view all the answers

Study Notes

Circles

Definition

A circle is a set of points in a plane that are equidistant from a fixed point called the center.
All points on the circle are equal distance from the center.

Characteristics

A circle is a closed curve.
A circle has no beginning or end.
A circle is a two-dimensional shape.

Properties

Circumference: The distance around the circle.
Diameter: The longest distance across the circle, passing through the center.
Radius: The distance from the center to any point on the circle.
Center: The fixed point equidistant from all points on the circle.

Formulas

Circumference (C) = 2 × π × radius (r)
Diameter (d) = 2 × radius (r)
Area (A) = π × radius^2 (r^2)

Semi-Circle Connection

A semi-circle is a half circle, formed by dividing a circle into two equal parts.
A semi-circle has the same center as the original circle.
The circumference of a semi-circle is half the circumference of the original circle.

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Description

Test your knowledge of circles, including their definition, characteristics, and properties such as circumference, diameter, radius, and center. Learn formulas and relationships between these elements and how they apply to semi-circles.