Circle
set of all points equidistant from a given point called the center of the circle
A circle is a two-dimensional shape that is defined as the set of all points in a plane that are equidistant from a fixed point called the center of the circle. The distance from the center of the circle to any point on the circle is called the radius, which is denoted by the letter r. Alternatively, the diameter of a circle is defined as the distance across the circle through its center, and is equal to twice the radius.
Some important properties of a circle include:
1. Circumference: The circumference of a circle is the distance around it, and is equal to 2πr (where π is the irrational number pi, approximately equal to 3.14). Alternatively, the circumference can be calculated using the formula C = πd, where d is the diameter of the circle.
2. Area: The area of a circle is the amount of space enclosed by it, and is equal to πr^2.
3. Chord: A chord is a line segment joining two points on the circumference of a circle. The longest chord in a circle is the diameter.
4. Tangent: A tangent is a line that touches the circle at exactly one point, called the point of tangency.
5. Arc: An arc is a portion of the circumference of a circle. The length of an arc is proportional to the size of the angle it subtends at the center of the circle.
Circles are used in many areas of mathematics and science, including geometry, trigonometry, and physics. They are also commonly used in engineering and design, as circular shapes are often the most efficient for many applications.
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