Circle is a **set of points equidistant from the fixed central point**

**For Example**

Given above is the example of circle.

Note that every point on the circle is equidistant from the central point O

**Structure of Circle**

All circle contain following components:

(a) Center

(b) Radius

(c) Diameter

(d) Chord

(e) Arc

**(a) Center of Circle**

It is the fixed point located inside the circle.

All the points located on the circle are equidistant from the center.

In the above figure O is the center of the circle, which is located inside.

All the points on the circle (point A, B, C, D) are equidistant from point O

**(b) Radius of the circle**

The line from center to any point on the circle is called Radius

For a circle, the length of radius is constant

Given above is the circle with center O with point A & B on the circle.

The line OA & AB are the radius of circle.

Note the length of radius OA & OB is same because the value of radius is constant for any circle

**(c) Diameter of circle**

Its a straight line meeting two ends of circle and passing through point O

Given above is the image of circle with center O

Here line AO is the radius of the circle which is extended to reach other side of circle at point B.

Hence AB is diameter of circle as its a straight line meeting two ends of circle at point A & B and passes through center O.

Note that its twice the length of radius

Diameter = 2 x Radius

Important points about diameter

(i) It’s a straight line

(ii) It passes through center O

(iii) touch the two opposite ends of circle

(iv) its length is twice the radius

You can draw multiple diameter in any given circle

Given below is the circle with center O

The line AB, CD and EF are the diameter of the circle

**(d) Chord **

Line segment joining any two points of the circle is called Chord

Diameter of the circle is the longest chord

Given above is the circle with center O

Here AB, CD and EF are the chords joining two different points on the circle.

The line CD is also called diameter as it joins two opposite points on circle while passing through center O

**(e) Arc**

Any selected boundary of circle is known as Arc of circle

Given above is the circle with center O

Here the arc AB is the part of the circle between point A & B

**(f) Circumference of circle**

The length of the boundary of the circle is called circumference of circle

**Finding circumference using ruler**

Imagine a black wire in the form of circle.

Now if you twist the wire into straight line and find the length using ruler, you will get the circumference of the circle

**Questions on Circle**

**(01) Study the image below and find the name of the diameter**

Here AB is the diameter of circle as it passes through center O

Rest of the lines EF & CD are the chords

**(02) Study the figure and find the length of radius**

Given line AB is the diameter as it passes through center O of circle

Length of diameter AB = 8 cm

We know that diameter is twice the radius

Radius = diameter / 2

Radius = 8 / 2

Radius = 4 cm

**(03) Study the figure below and find the length of line OD**

Solution

Here both OA & OD are the radius of circle.

We know that for a given circle the length of the radius is the same

OA = OD = 2 cm

**(04) A wire of 8 cm is folded to form a circle****What is the circumference of circle**

Since the wire is folded to form a circle, the circumference of the circle will also be 8 cm

**(05) Study the circle below and find the length of its diameter**

In the above image:

AB is the chord and OD is the radius of circle

We know that:

Diameter = 2 x Radius

Diameter = 2 x 4

Diameter = 8 cm

**(06) Observe the below image of circle and mention the name of radius, diameter and chord**

Radius = OD

Diameter = EF

Chord = AB & EF

**(07) What is the line EF**

(a) Diameter

(b) Chord

(c) Radius

EF is a line touching two ends of the circle but doesn’t pass through center.

Hence its a chord**Option (b) is correct**

**(08) What is the line AB in below circle**

(a) Diameter

(b) Radius

(c) Chord

AB is a line that touches circle at end point and also passes through center.

Hence AB is a diameter

Option (a) is the right answer

**(09) What is the line OE**

(a) Chord

(b) Radius

(c) Diameter

The line OE is a line from center O to point E on the triangle.

Hence it is a Radius**Option (b) is the right answer**

**(10) What is the length of line OF**

Solution

AB is the diameter of circle length 10 cm

OF is the radius

We know that:

Radius = Diameter / 2

Radius = 10 / 2

Radius = 5 cm

Hence length of OF is 5 cm