# Radius is half of Diameter

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

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

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;

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

We know that:
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

We know that:

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

Solution
Diameter = 7 cm

We know that:

(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 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 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 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:

Hence the radius of circle is 3 cm

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

Solution
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 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