7. Circumference of a circle

Circumference of a circle

Circle radius,diameter and chord

The segment joining the center to a freely chosen point on the circumference is called the radius. We usually denote radius by the lowercase r or the uppercase R.
The  segment that joins the two points of the circle is called a chord.
The chord passing through the center of the circle is called the diameter.
AO=BO=EO=FO as circular radii.
The radii EO and FO form the diameter EF.
BC is a chord.

Parts of the circle
Diameter of Circle:

The distance across the circle. The length of any chord passing through the center. It is twice the radius.
Diameter = 2⋅Radius = 2r
Radius of circle:
The radius is the distance from the centre to any point on the circle.
Radius is also known as half  of the diameter.
Radius=Diameter/2
Chord:
The segment that joins the two points of the circle is called a chord.

A circle

Compass can look different, but all whips have two legs - a sharp-pointed pin and a pencil. 
Compass can be used to draw a circle.
If you mark a small mark or dot on a piece of paper and place the sharp crank leg at that point, you can draw a circle. The dot is called the center of the circle, and we usually denote by the capital letter O.
The segment joining center O of a circle to a point on the circle (point A in the drawing) is called the radius.

Circle circumference

Circumference of a circle is the actual distance around it.
Ratio of the circumference and the diameter of a circle is a constant
The numerical value of π is taken as (frac{22}{7}) or 3.14. (approximate)
Circumference of a circle = 2πr, where r is the radius of the circle
All circles are similar to one another. So, the ratio of the circumference to that of diameter is a constant,
That is CircumferenceDiameter=constant(piπ)    
Therefore Cd=π (Where the approximate value of π is 3.14)  
C=  d⋅π  or C= d⋅3.14
The diameter is twice the radius (2r), so the above equation can be
written as C=2r⋅π Note: d=2r
Therefore, the circumference of a circle, C=2πr units.   

Position of two circles in a common point

1. The circles have no common points, and they are inside each other. 
2. The circles have one common point, touching them externally. 
3. The circles have one common point (B), and they touch internally.
4. circles have no common points, and they are off each other