Circle

A circle is a two-dimensional shape that is perfectly round and is defined as the set of all points in a plane that are a fixed distance, called the radius, from a given point, called the center. The distance across the circle passing through the center is called the diameter.

Key Concepts:

• Radius: The distance from the center of the circle to any point on the circle.
• Diameter: The distance across the circle passing through the center, which is twice the length of the radius.
• Circumference: The perimeter of the circle, which is equal to the distance around the circle and is found using the formula: C = 2πr or C = πd, where π (pi) is a constant approximately equal to 3.14159.
• Area: The amount of space inside the circle, which is found using the formula: A = πr2, where r is the radius of the circle.

Properties:

• A circle has an infinite number of lines of symmetry, all passing through its center.
• The radius of a circle is always perpendicular to the tangent at the point of contact on the circle.
• The area of a circle is maximized for a given perimeter, making it the most efficient shape for enclosing a given area.

Examples:

Here are a few examples of real-life objects that can be represented by circles: coins, wheels, plates, and the face of a clock.

Understanding the properties and formulas associated with circles can help in solving various mathematical problems and real-world applications.

[Circle] Related Worksheets and Study Guides:

• Diameter of CircleMathematics • Sixth Grade
• Word FamiliesEnglish Language Arts • Kindergarten