What Is a Circle?
What Is a Circle?
A circle is a shape containing a set of points that are all the same distance from its center.
The Oxford English Dictionary defines a circle as "a plane figure bounded by a single curved line, called the circumference, which is everywhere equally distant from a point within, called the centre. But often applied to the circumference alone, without the included space."
Parts of a Circle
The circle technically refers to the boundary of the shape (that is the curved blue line).
The center is a point inside the circle. All points on the circle are the same distance from the center.
Radius, Diameter and Circumference
The most important lengths in a circle are the radius, the diameter and the circumference.
The radius is the line segment from the center of the circle to any point on the circle.
The radius also refers to the length of this line. The radius is usually denoted by the symbol r.
The diameter is the line segment that contains the center of the circle and has its endpoints on the circle.
The diameter also refers to the length of this line. The diameter is usually denoted by the symbol d.
The diameter is twice the length of the radius. d = 2r
The circumference is the distance around the circle.
The circumference is usually denoted by the symbol C.
The circumference is π × the length of the diameter. C = πd.
Other Parts of a Circle
A chord is a line whose endpoints lie on the circle.
Note: The diameter is the chord that contains the center.
An arc is a portion of the circle.
A tangent is a line that touches the circle at one point.
A sector is a region bounded by two radii and the arc lying between the radii.
A sector looks like a slice of cake.
A segment is a region, not containing the center, bounded by a chord and an arc lying between the chord's endpoints.
Properties of Circles
Circumference of a Circle
The circumference of a circle is found using the formula:
In the formula, π (pi) ≈ 3.14 and d is the diameter of the circle. The image above shows what we mean by the diameter.
Area of a Circle
The area of a circle is found using the formula:
In the formula, r is the radius of the circle. The image above shows what we mean by the radius.
Equation of a Circle
The equation of a circle is:
In the equation, (x, y) are the Cartesian coordinates of the points on the circle. (a, b) are the Cartesian coordinates of the center of the circle and r is the radius of the circle.
The image below shows what we mean by a point on the circle, the center and the radius of the circle:
There are several theorems about circle geometry.