Circles, Definition of a Circle, Terms Related to a Circle

# Circles, Definition of a Circle, Terms Related to a Circle

## Definition of a Circle

A circle is the locus of all those points which are equidistant from a fixed point on a given plane. The fixed point is called the center of the circle.
The distance between the center of the circle and any point on the circle is called the radius of the circle. In the given figure below, OA is a radius of the circle.
A line segment passing through the center and touching the circle at two points is called the diameter of the circle.
The diameter is twice of the radius, i.e., diameter, d = 2 × radius = 2r.

## Terms Related to a Circle

A line segment joining the centre of a circle to any point on the circle is called the radius of the circle. In the following figure, OA is the radius of the circle. The radius of a circle is half of the diameter of the circle. Radius, r = d/2

Diameter of a Circle

A line segment joining any two points on the circle and passing through the centre is called the diameter of the circle. The diameter of a circle is twice the radius of the circle.
Diameter, d = 2r

### Interior and Exterior of a Circle

Consider a circle with center O and radius r. The circle divides the plane into three parts.
1.      The part of the plane consisting of point A for which OA < r, lies in the interior of the circle.
2.      The part of the plane consisting of point B for which OB = r, lies on the circle itself.
3.      The part of the plane consisting of point C for which OC > r, lies in the exterior of the circle.

### Circular Region

The part of the plane consisting of the circle and its interior is called the circular region.

### Circumference

The length of the boundary of the circle is called the circumference. If the radius of a circle is r, then the circumference of the circle is given by 2Ï€r.

### Chord of a circle

A chord is a line segment whose end points lie on the circumference. EF is a chord of the circle.

### Arcs of a circle

Any part of the circumference of a circle is called an arc of the circle. The curved part ECF is an arc of the circle.

### Major arc and Minor arc

A chord that does not pass through the center divides the circumference into two unequal arcs. The greater arc is called the major arc. The smaller arc is known as the minor arc. In the figure, ECF is the minor arc and EAPQBF is the major arc.

### Sectors of a circle

The region encloses between two radii OP and OQ and the arc PQ is known as a sector of the circle. The smaller region intercepted by the arc PQ is known as the minor sector. The larger region intercepted by the arc PAEFBQ is known as the major sector. The angle POQ is called the angle of the sector.

### Angle in a semicircle

It is an angle subtended by the diameter at any point on the circumference of the semicircle. This angle is always a right angle, i.e., 90°.

### Segments of a circle

The part of the circle enclosed by an arc and the corresponding chord is called a segment. A chord divides the region of the circle into two parts. The smaller part is called the minor segment and the larger part is called the major segment.

If the sector is equal to the one-fourth of the circle, it is called the quadrant of the circle. In the given figure, two perpendicular radii enclose the quadrant of the circle. A circle has four quadrants.

### Secant

A line which intersects the circle at two distinct points is called a secant of the circle. Line AB ­is a secant to the circle and line segment PQ is a chord to the circle.

### Tangent

A line which touches the circle at only one point is called a tangent. In the given figure, line l is the tangent to the circle with center O. The tangent to a circle is a special case of the secant, when two end points of its corresponding chord coincide.

### Concentric Circles

The circles with the same center and different radii are called concentric circles. Concentric circles do not intersect.