## circle

### A circle is a closed curved shape in which all points on the boundary are equidistant from the center

A circle is a closed curved shape in which all points on the boundary are equidistant from the center. It is a two-dimensional figure with no corners or edges. The distance from the center of the circle to any point on its boundary is called the radius.

Key features of a circle include:

1. Center: The point in the middle of the circle from which all points on the boundary are equidistant. It is often denoted as (h, k) in coordinate geometry.

2. Radius: The distance from the center of the circle to any point on its boundary is called the radius. The length of the radius is denoted by “r”.

3. Diameter: The diameter of a circle is a straight line passing through the center and touching two points on the boundary. It is always twice the length of the radius (d = 2r).

4. Circumference: The circumference of a circle is equal to the distance around the boundary of the circle. It can be calculated using the formula: C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159.

5. Area: The area of a circle is the amount of space enclosed by its boundary. It can be calculated using the formula: A = πr^2, where r is the radius of the circle.

6. Chord: A chord is a straight line segment that connects two points on the boundary of a circle.

7. Arc: An arc is a part of the boundary of a circle, defined by two endpoints and the curve connecting them.

In geometry, circles have various applications and properties. They are commonly used in construction, measurements, and calculations in fields like architecture, physics, and engineering.

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The Properties and Relationships of Chords in Mathematics | A Comprehensive Guide to Understanding Chords in Circles