Circle
A circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the center.
Circles are simple closed curves which divide the plane into an interior and exterior. The circumference of a circle means the length of the circle, and the interior of the circle is called a disk. An arc is any continuous portion of a circle.
The ratio of the circumference C to diameter d of a circle is the constant π (Greek letter pi). The number π is irrational, and consequantly, a nonrepeating and nonterminating decimal:
Circumference:
C = 2πr where r = radius of circle and π ≈ 3.14159...
Diameter:
The diameter of a circle is a straight line through the center of the circle touching the circle at both sides.
The diameter, d, of a circle is double its radius:
The area enclosed by a circle is the radius squared, multiplied by π:
A circular sector or circle sector also known as a "pie piece" is the portion of a circle enclosed by two radii and an arc.
Let θ be the central angle, in radians, and r the radius. The total area of a circle is πr2. The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and 2π (because the area of the sector is proportional to the angle, and 2π is the angle for the whole circle):
In addition, if θ refers to the central angle in degrees, a similar formula can be derived.
A = πr2 · (θ/360)
Let R be the radius of the circle, c the chord length, s the arc length, h the height of the segment, and d portion. The the height of the triangulararea of the circular segment is equal to the area of the circular sector minus the area of the triangular portion. In the illustration provided below, the circular segment is represented by the yellow colored portion.
The radius is R = h + d
The arc length is s = Rθ, where θ is in radians