What is a Circle?
A circle is a collection of all points in a flat plane that are at a constant, fixed distance from a fixed point in that same plane. Think of a giant Ferris wheel, a round dinner plate, a coin, or the boundary left behind when you trace a roll of tape with a pencil. The fixed point right in the middle is called the center of the circle.
To master circles, you need to speak the language of geometry. Here are the core terms you need to know:
- Radius: A straight line segment connecting the center of the circle to any point on its outer boundary.
- Chord: A straight line segment whose two endpoints both lie on the circle's outer boundary.
- Diameter: A special chord that passes directly through the center of the circle. It is the longest possible chord in any circle and is exactly twice the length of the radius.
- Secant: A straight line that cuts completely through a circle, intersecting it at exactly two points. Unlike a chord, a secant extends infinitely outside the circle.
- Arc: A continuous portion or piece of the circle's outer curved boundary. A small piece is called a minor arc, while a large piece is called a major arc. Half a circle's boundary is called a semicircle.
- Sector: The region enclosed between two radii and an arc. Think of this as a slice of pizza or cake.
- Segment: The region enclosed between a chord and an arc.
Let us compare the two regional parts of a circle to prevent confusion:
| Feature | Sector | Segment |
|---|---|---|
| **Real-life Shape** | A slice of pizza or watermelon wedge | A flat slice cut off the edge of a round cookie |
| **Center connection** | Directly touches the center vertex | Does not need to touch the center point |