**Proof of Circumference of a Circle**

- We know that, circle is the locus of points which are at equal distance from the fixed point.
- The fixed point is called as the center of circle and the locus of points is called as the circumference of the circle.
- The following figure shows the circle with center
**O**and radius

- Now, the length of the total arc forming the circle is called as the circumference of the circle.
- While finding the formula of circumference of circle the constant π was invented.
- Now, if we cut the circle then we can see that it become a simple straight line with length equal to circumference of circle.
- Let us consider circle 1, 2, 3 with different radius and circumference. When we cut the circle it simply the straight wire length which is the circumference of the circle as shown in figure.

- In above figure, we can see that when we cut a circle then it forms the straight line whose length is equal to circumference of circle.
- And if we take the ratio of circumference and diameter of circle in each circle then it will be the constant and the value of that constant is 22/7.
- And this value 22/7 is denoted by Greek letter π.

Thus, here

Circumference of circle/ diameter of circle = 22/ 7 = π

Hence, circumference of circle = diameter of circle *π

Circumference of circle = 2*r*π

Thus,

Circumference of circle = 2*π*r

Circumference of circle/ diameter of circle = 22/ 7 = π

Hence, circumference of circle = diameter of circle *π

Circumference of circle = 2*r*π

Thus,

Circumference of circle = 2*π*r