Circles: Definition, Characteristics, and Properties

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.

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.