Circle

A circle is a locus of points in a plane equidistant from a given point (center of a circle). The distance between any point of the circle and its center is called the radius of the circle (the radius is denoted by the letter R).
This means that a circle is a line on a plane, each point of which is located at the same distance from the center of the circle.

A circle is a part of a plane bounded by a circle and including its center.

A segment connecting two points of a circle is called a chord. The chord passing through the center of the circle is the diameter. The diameter of the circle is equal to its doubled radius: D = 2R.

See online calculator - Circle Length Calculator.

The intersection point of two chords divides each chord into segments, the product of which is the same: a1a2 = b1b2

The tangent to the circle is always perpendicular to the radius drawn to the tangent point.

Segments of tangents to the circle drawn from one point are equal: AB = AC, the center of the circle lies on the bisector of the angle BAC.

The square of the tangent is equal to the product of the secant and its outer part

The center angle is the angle whose vertex coincides with the center of the circle.

An arc is the part of a circle between two points.

The measure of an arc (in degrees or radians) is the central angle that rests on that arc.

An inscribed angle is an angle whose vertex lies on a circle and the sides of the angle intersect it.

The inscribed angle is half the central angle if both corners rest on the same circular arc.
The interior angles that rest on the same arc are equal.

A sector of a circle is a geometric figure bounded by two radii and an arc on which these radii are based.

Sector perimeter: P = s + 2R.

Sector area: S = Rs / 2 = ПR2а / 360 °.

A segment of a circle is a geometric figure bounded by a chord and an arc contracted by it.