Introduction of Circle and Related terms of circle

Circle

A Circle is a collection of those points in a plane that are at a given constant distance from a given fixed point in the plane. The fixed point is called the center of the circle (O) and the given constant distance is called the radius of the circle (r), denoted by C(O, r). 

Diameter of a circle

A straight line segment which starts from one end of a circle and after passing through the center of the circle reaches the other end of the circle.

Circumference of circle 

The distance around a circle. It is the boundary length of circle.

Concentric circles 

Circles having the same center but with different radii are said to be concentric circles.

Arc of a circle 

A part or piece of the circle is an arc of the circle. Let A, B, C, D are four points on the circumference of a circle. Then, the parts AB, BC, CD and DA are arcs. Arcs are symbolically written as $\overset\frown{AB},\overset\frown{BC},\overset\frown{CD},\overset\frown{DA}.$

Length of an arc 

The length of an arc $\overset\frown{AB}$ is the length of that part of circle which is AB. It is represented as $l(\overset\frown{AB})$.

Central Angle 

The angle made at the center of the circle is central angle $\angle AOB$ .

Minor Arc 

A minor arc is the smaller part of the circle. 

Major Arc 

A major arc is the larger part of the circle.

Degree measurement of an arc 

The degree measurement of a minor arcs is the measure of the central angle containing the arc and that of a major arc is $360{}^\circ $ minus the degree measure of the corresponding minor arc.
The degree measurement of an arc $\overset\frown{AB}$ is denoted by $m(\overset\frown{AB})$. Here $m(\overset\frown{AB})=75{}^\circ$ and  $m(\overset\frown{BA})=285{}^\circ $.

Chord 

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

Diameter is also defined as a chord passing through the centre of a circle is called diameter
A diameter is the longest chord of the circle.
If d is diameter of the circle C(O, r), then d = 2r.

Semi-circle 

A diameter divides a circle in two equal parts. Each of these two arcs are called semi-circle.

Segment of a circle 

A chord divides a circle in two parts. The regions enclosed by the chord and arc is called segment of the circle.

Minor segment

The segment containing minor arc and chord.

Major segment 

The segment containing major arc and chord.

Sector 

A region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called a sector.

Minor sector 

A region in the interior of minor arc and a pair of radii.

Major sector 

A region in the interior of major arc and a pair of radii.

Formulas of circle

• Perimeter of circle = $2\pi r$

• Area of circle = $\pi {{r}^{2}}$

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