A circle is the set of all points in a plane that are the same distance, called the radius, from a central point. The distance across the circle through the center is called the diameter and equals twice the radius. The circumference, or distance around the circle, is given by C = 2πr or equivalently C = πd. The area enclosed by the circle is A = πr², which can also be written as A = π(d/2)² using the diameter. These two formulas are the foundation for nearly every other circle calculation.
Several important line and segment types interact with circles. A chord is a line segment whose two endpoints both lie on the circle, and the longest possible chord in any circle is the diameter. A tangent is a line that touches the circle at exactly one point, called the point of tangency, and a tangent is always perpendicular to the radius drawn to that point. A secant is a line that intersects the circle at exactly two points and, unlike a chord, extends infinitely in both directions beyond the circle.
Arcs and angles have rich relationships inside a circle. A central angle has its vertex at the center of the circle and its sides are radii; the measure of a central angle equals the measure of its intercepted arc. An inscribed angle, by contrast, has its vertex on the circle and its sides are chords, and it always measures half of the central angle that subtends the same arc. This also means that an inscribed angle is exactly half the measure of its intercepted arc. The arc length along a curved section is s = (θ/360°) × 2πr when θ is measured in degrees, or s = rθ when θ is in radians. The area of a sector (the pie-slice region bounded by two radii and an arc) is A = (θ/360°) × πr², which represents the same fraction of the whole circle as the central angle does of 360°.