# Parts of a Circle

A circle is a set of points in a plane that are equidistant from a point called the center of the cicle . In the figure below, \( O \) is the center of the circle and points \( A \), \( B \) and \( C \) are points on the circle at the same distance \( r \) from the center \( O\).

The radius of a circle is the line segment from any point on the circle to the center of the circle. In the diagram above, \( OA \), \( OB \) and \( OC \) are radii having the same length \( r \).

The circumference of a circle is the perimeter of the circle or the total distance around the curved edge of a circle.

The formula of the circumference \( C_i \) of a circle of radius \( r \) is given by \[ C_i = 2 \pi r \]

The formula of the area \( A \) of the surface enclosed by a circle of radius \( r \) is given by \[ A = \pi r^2 \]
A chord of a circle is any line segment joining two points that are on the circle. In the figure below, \(AB\) , \( EF \) and \( CD \) are chords of the circle.

A diameter of a circle is a chord through the center of the circle. In the figure below, \( EF \) is a diamter of the circle. The length of the diameter is equal to \( 2 r \), twice the length of the radius.

An arc of a circle is a portion of a circle. In the figure below, two points \( A \) and \( B \) splits the circle inro two arcs with the small one called the minor arc and the large one called the major arc. The symbol \( \overset{\LARGE\frown}{} \) is used above letters to represent an arc as follows: \( \overset{\LARGE\frown}{AB} \).

A central angle of a circle is an angle whose vertex is the center of the circle and whose legs are two radii. In the figure above, \( \theta \) is a central angle.

The length \( S \) of an arc corresponding to a central angle \( \theta \) and in a circle of radius \( r \) is given by \[ S = \theta r \quad \text{with} \; \theta \; \text {in radians} \]

A sector is a part of the circle enclosed by an arc and two radii. In the figure below, the blue surface is a sector.

The area \( A \) of a sector whose central angle \( \theta \) and radius \( r \) is given by \[ A = \dfrac{1}{2} \theta r^2 \quad \text{with} \; \theta \; \text {in radians} \]

A straight line that touches a circle at one point is called tangent to a circle as shown in the figure below. The tangent \( T \) touches the circle at the point of tangency \( P \).

## More References and Links

The Four Pillars of Geometry - John Stillwell - Springer; 2005th edition (Aug. 9 2005) - ISBN-10 : 0387255303Geometry Tutorials, Problems and Interactive Applets