Definition of a Circle
The definition of a circle is a Grade 7 geometry concept in Big Ideas Math, Course 2. A circle is the set of all points in a plane that are equidistant from a fixed center point. The distance from the center to any point on the circle is the radius (r). The diameter (d) crosses the circle through the center, equaling twice the radius: d = 2r. The circumference (distance around the circle) is C = 2πr or C = πd. The area enclosed is A = πr². These formulas derive directly from the definition of constant distance from the center, making the radius the key measurement for all circle calculations.
Key Concepts
A circle is the set of all points in a plane that lie at a given distance from a fixed point. The fixed point is called the center of the circle, and the distance from the center to any point on the circle is called the radius.
Common Questions
What is the definition of a circle?
A circle is the set of all points in a plane that are the same distance (the radius) from a fixed center point.
What is the radius of a circle?
The radius is the distance from the center of the circle to any point on the circle. All radii of the same circle are equal in length.
What is the relationship between the diameter and the radius?
The diameter passes through the center and connects two points on the circle. It equals twice the radius: d = 2r, or equivalently r = d/2.
What is the formula for the circumference of a circle?
C = 2πr or equivalently C = πd, where r is the radius and d is the diameter. Use approximately 3.14 or the π key for calculations.
What is the formula for the area of a circle?
A = πr², where r is the radius. Square the radius first, then multiply by π.
How does the definition of a circle (equidistant points) explain why C = 2πr?
The circumference is the boundary traced at constant distance r from the center. The ratio of circumference to diameter is always π, giving C = πd = 2πr.