In this post we will discuss the concept of circle and its important properties. We have tried to covered the topic in as simple manner as possible so that it does not get boring, also we have tried to incorporate drawings and illustration for better understanding of concepts.

Some of the concept covered in this chapter is:

1.What is circle

2. Different parts of circle

3. Important properties of circle

4. Questions related to circle

**What is a circle?**

A circle is a set of points in a plane, all of which are the same distance from a given point, called the center. A circle is named by its center

Here, the circle is called circle O

Point O is the center of the circle O

All the points X, Y, Z, P and Q are at same distance from the center O

## Different Parts of circle

In order to fully understand the concept of circle, we first need to understand its component. In this section we will discuss the different parts of circle with the help of diagram

**Centre of the circle **

The center of the circle is the point which is equidistant from all the points on its circumference.

In the figure, Point O is the center of the circle.

**Radius of a circle **

** **A straight line joining the center of the circle with any point on its circumference is called radius of the circle.

In the figure, OC is the radius of the circle.

**Diameter** **of circle **

The diameter is the length of the line through the center that touches two points on the edge of the circle

In the figure, AC is the diameter of the circle.

**Relation between diameter and radius**

The length of the diameter (d) is twice the length of the radius (r).

i.e., length of Diameter = 2 x length of radius

d = 2 x r

**Sector of the circle **

A sector is the portion of a disk enclosed by two radii and an arc in a circle

**Ex –** AOC is the sector of the circle (the green shaded portion of the given figure).

In the figure, AOC is the sector of the circle

**Segment of the circle **

** **A segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord

**Ex – **PQ is the segment of the circle (the green shaded portion of the given figure).

In the figure, PQ is the segment of the circle

**Arc of a circle **

Any portion of the circumference of a circle is called an arc of a circle

**Note –** An arc that connects the endpoints of a diameter has a measure of 180° and is a semicircle.

In the figure, the arc AC connects the end-points of diameter of the circle i.e., AC. So, AG is a semicircle as measure of arc AG = 180°

**Chord **

The *chord of a circle* is the line segment joining any two points on the circumference of the circle.

In the figure, XY is the chord of the circle

Note: Remember that chord do not pass through the center of the circle, otherwise it will be called diameter

**Central angle **

A central angle has its vertex at the center of the circle

In the figure, **∠**APC is the central angle of the circle.

**Tangent **

A line that touches the circumference of a circle at a point is called the tangent. A tangent is always perpendicular to its radius

In the figure, AB is the tangent of the circle which is perpendicular to the radius OC

**Important Properties of circle**

Below are some of the properties of circle. These properties are important as they will help to solve questions related to circle, so please make an effort to understand and remember each of the properties

1. If two circles are of equal radii, then they are called congruent circles

Above both the circles have similar radius, hence they are called congruent circle

2. If two circles are of different radii, they are called similar circles

Above both the circles are of different radius, hence they can be termed as similar circles.

3. The radius drawn perpendicular to the chord bisects the chord

In the above figure, you can see that;

AC is the chord of the circle and OB is the radius of circle perpendicular to the chord.

Now according to the property of circle, the radius OB will bisect the chord AC such that AB = BC

4. The chords that are equidistant from the center are equal in length

In the above figure you can see that AB and CD are the chords of circle which is equidistant from the center of circle O.

According to property of circle, any chords which are equidistant from the center are equal in length.

Hence AB = CD

5. The diameter of a circle is the longest chord of a circle

6. The distance from the center of the circle to the longest chord (diameter) is zero

7. The perpendicular distance from the center of the circle decreases when the length of the chord increases

From the above figure you can see that as the chord move towards the center of the circle, its length increases.

8. If the tangents are drawn at the end of the diameter, they are parallel to each other

From the above figure you can see that

OA and OB are the radius of the circle and CD and EF are tangents that are parallel to each other

## Formulas of circle

**Area of a circle**, A = πr^{2} square units**Perimeter or circumference of circle** = 2πr units = πd

Where,

Diameter = 2 x Radius

d = 2r

Here “r” represents the radius of a circle.

**Question (Type I)**

**Q) Find the circumference and area of a circle having radius = 7 cm.**

Sol. Given, radius = 7 cm

Area of a circle, A = πr^{2}

A = 22/7 x (7)** ^{2} = **22 x 7 = 154 square cm.

Perimeter or circumference of circle, P = 2πr

P = 2 x 22/7 x 7 = 44 cm

**Question (Type II)**

**Q) Find the circumference and area of a circle having diameter = 14 cm.**

Sol. Given, diameter = 14 cm.

Therefore, radius = diameter/2 = 14/2 = 7 cm

Area of a circle, A = πr^{2}

A = 22/7 x (7)** ^{2} = **22 x 7 = 154 square cm.

Perimeter or circumference of circle, P = 2πr

P = 2 x 22/7 x 7 = 44 cm