**What is a radius of circle?**

Radius is the line joining from center to point on circle.

In a particular circle, there can be many radius but they have same length

**Example of Radius**

Given above is the image of a circle with center O

Here OA, OB, OC and OD are the radius since they are straight line joining the center and circle.

Its given that OA = 4 cm

Since, value of all radius are same, we get:

OA = OB = OC = OD = 4 cm

**What is diameter of circle?**

Diameter is a straight line joining two points on a circle while passing through center O.

In a circle there can be multiple diameters and there length will be same.

There are two important points about diameter

(a) It passes through center

(b) Its end points lie on the circle

**Example**

Above image is of circle with center O.

Here AB and CD are the diameters of the circle because:

(a) they are straight line

(b) passes through center

(c) end points of the line are on circle’s boundary

**Diameter and Radius Relationship**

Above image is of circle with center O.

Here AB is the radius of the circle.

If you observe carefully you will find that the diameter is made by joining two different radius

Hence,

AB = OA + OB

AB = r + r**AB = 2r**

Hence the diameter AB is twice the radius.

Thus; **Diameter = 2 x Radius**

This is one of the important property of circle.

Remember this formula as it would help us to solve multiple problems in the future

Let us now solve some questions related to the concept

**(01) The radius of circle is given 6 cm. Find the length of the diameter.**

**Solution**

Radius = 6 cm

We know that:

Diameter = 2 x Radius

Diameter = 2 x 6

Diameter = 12 cm

**(02) Find the length of line OC**

**Solution**

AB is the diameter of circle with length 8 cm

OC is the radius

We know that:

Radius = Diameter / 2

Radius = 8 / 2

Radius = 4 cm

**(03) Find the value of radius if diameter is 7 cm **

**Solution**

Diameter = 7 cm

We know that:

Radius = Diameter / 2

Radius = 7 / 2

Radius = 3.5 cm

**(04) Observe the below figure and find diameter of circle**

**Solution**

OA is the radius of circle

OA = 6 cm

We know that

Diameter = 2 x Radius

Diameter = 2 x 6

Diameter = 12 cm

**(05)Observe the below figure and fill in the blanks**

(a) Radius of circle is __________

(b) Diameter of circle is _________

**Solution**

(a) Radius of circle is 12 cm

(b) Calculating diameter

Diameter = 2 x Radius

Diameter = 2 x 12

Diameter = 24 cm

Diameter of circle is 24 cm

**(06) Find the length of line CD**

**Solution**

OA is the radius of the circle

OA = 5 cm

CD is the diameter of circle

We know that:

Diameter = 2 x Radius

Diameter = 2 x 5

Diameter = 10 cm

Hence length of CD = 10 cm

(07) Find the length of radius of below circle

Here CD and EF are the chords of the circle

AB is the diameter as it passes through center O

We know that:

Radius = Diameter / 2

Radius = 6 / 2

Radius = 3 cm

Hence the radius of circle is 3 cm

**(08) Radius of circle is 3.5 cm. Find the diameter**

Solution

Diameter = 2 x Radius

Diameter = 2 x 3.5

Diameter = 7 cm

Hence diameter is 7 cm

**(09) Study the figure below and find the length of segment BC **

**Solution**

The figure is of circle with center O.

Here OA is the radius of the circle with length 3 cm

OA = 3 cm

Segment BC is also the diameter of the circle

We know that:

Diameter = 2 x Radius

Diameter = 2 x 3

Diameter = 6 cm

Hence the length of side BC = 6 cm

**(10) Find the radius of below circle if the length of following segments are given:**

AB = 2.5 cm

EF = 6 cm

CD = 2. cm

**Solution**

AB & CD are the chords of the circle

EF is the diameter

EF = 6 cm

We know that

Radius = Diameter / 2

Radius = 6 / 2

Radius = 3 cm

Hence the radius of circle is 3 cm