What is a Circle?

A circle is a two-dimensional plane geometrical figure which is a closed region. A circle can be defined as a set of points adjacent to each other and are equidistant from a fixed point. There is a wide range of examples for the circular objects in and across our surroundings. A few examples of circular objects are:

Bangles used as ornaments

The base of a tumbler

The lower end of the cone

Top and bottom of cylinders

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Regions of Circle:

The circle has three regions as in every closed geometric figure. A point can lie on any of the three regions of the circle namely:

Interior of the Circle:

The region inside the boundary of the circle is called its interior and the point lying in this region is called the interior point.

Exterior of the Circle:

The region outside the boundary of the circle is called the exterior of the circle and any point lying outside the circle is said to be in its exterior.

On the Circle:

Any point on the boundary of the circle is said to be on the circle. The point on the circle coincides with any one of the points that constitute the circle.

Parts of the Circle:

A circle is an interesting plane geometric figure which has at most importance in mathematics. It represents the atom which is the basic constituent of the universe and the entire universe is also represented by the circle. Spiritually, the circle is used to represent that everything in the materialistic world is ultimately zero (0). The circle has many parts which include:

Centre: A center of the circle is that point from which all the points that constitute a circle are equidistant. It is generally represented by the letter ‘O’.

Circumference: The region enclosed by a circle or the length of the boundary of the circle is called its circumference. Circumference of a circle is the measure of the total length of the circle which is equal to its perimeter.

Radius: The length of the line joining the center of the circle and any point on its circumference is called the radius of the circle. It is generally represented by the letter ‘r’.

Diameter: The line joining any two points on the circle passing through its centre is called the diameter of the circle. Diameter is represented by the letter ‘d’. The diameter of a circle is two times its radius.

Chord: Any line that touches the two points on the circle is called the chord of the circle. The diameter of a circle is its longest chord.

Arc: The portion of a circumference of the boundary of the circle is called its arc. The smaller portion of the circle’s boundary is called its minor arc and the larger portion is called the major arc.

Segment: The region of the circle enclosed by an arc and the chord is called the segment of the circle. The chord divides the circle into two segments. The region enclosed by a chord and the major arc is called the major segment and the region enclosed by the minor arc and the chord is called a minor segment.

Semicircle: The diameter divides the circle into two equal segments. Each segment is called the semicircle which is equivalent to half of the circle.

Sector: The region enclosed by two radii and an arc of the circle is called the sector of the circle. Any two radii divide the circle into two sectors. The region enclosed between the radii and the major arc is called the major sector and the region enclosed by the radii and the minor arc is called the minor sector.

Tangent: Tangent is the line that touches the circle at only one point on its boundary is called the tangent of the circle. Any point on the circumference of the circle has only one tangent.

Secant: The line passing through the circle at two different points is called the secant of the circle.

Area of a circle: The region enclosed by the surface of the circle on a plane is called its area.

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Important Formulae:

Circumference of the circle = 2 x π x radius

Diameter of the circle = 2 x radius

Area of the circle = π x radius x radius = πr2

Area of the sector of the circle is

A=\[\frac{θ}{360}\] x πr²

Area of segment of a circle = Area of sector - Area of triangle

Fun Quiz:

Are all Circles Similar?

Yes

No

Are all Circles Congruent?

Yes

No

How Many Tangents can be Drawn to a Circle from a Point at its Exterior?

One and only one

More than 4

Exactly two

How Many Secants can be Drawn to a Circle from a Point on its Exterior?

None

Two

One

More than 2

FAQ (Frequently Asked Questions)

1. What is a Circle? What are the Differences Between Concentric and Congruent Circles?

A circle is a closed geometric figure in a plane. All the points of the circle are equidistant from a fixed point. This fixed point is called the center of the circle. The line joining the center of the circle and any point on its circumference is called its radius. If the circles have the same point as its centre and the radius of the circles are different, then the circles are said to be concentric which means the same centre. If the circles have the same radius, however different points as centers, then the circles are called the congruent circles.

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2. How is a Circle Constructed using a Compass?

Compass is an instrument available with a geometry kit. It is generally used to draw perfect circles of the desired length. Before drawing a circle, the hinge at the top of the compass should be tightened so that it does not slip. The pencil is placed in the holder and the holder is tightened so that the pencil does not fall off. Pencil lead and the compass needle are aligned together and separated apart for the required length of the radius of the circle. The needle is pressed against a point on the paper and the knob at the top of the compass is turned such that the pencil tip touches the paper. The circle of the required radius is obtained.

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