# Circle and Related Terms

A circle is a collection of all points in a plane which are at a constant distance from a fixed point in the same plane. A line segment joining the centre of the circle to a point on the circle is called its radius. The length of the radius of a circle is generally denoted by the letter r.

Chord

A line segment joining any two points of a circle is called a chord.

Diameter

A chord passing though the centre of a circle is called its diameter. Diameter is the longest chord of a circle.

d = 2r

Arc

A part of a circle is called an arc.

Semicircle

A diameter of a circle divides a circle into two equal arcs, each of which is known as a semicircle.

Sector

The region bounded by an arc of a circle and two radii at its end points is called a sector.

Segment

A chord divides the interior of a circle into two parts, each of which is called a segment.

Circumference

The length of the boundary of a circle is the circumference of the circle.

The ratio of the circumference of a circle to its diameter is always a constant. This constant is universally denoted by Greek letter π.

c/d = π

π = 22/7

Concentric Circles

Circles having the same centre but different radii are called concentric circles.

Congruent Circles

Two cirlces (or arcs) are said to be congruent if we can superimpose (place) one over the other such that they cover each other completely.

Central Angle

The angle made at the centre of a circle by the radii at the end points of an arc (or a chord) is called the central angle or angle subtended by an arc (or chord) at the centre.

The length of an arc is closely associated with the central angle subtended by the arc.

Length of an arc = circumference × degree measure of the arc/360°

Inscribed Angle

The angle subtended by an arc (or chord) on any point on the remaining part of the circle is called an inscribed angle.