It we measure the circumference and diameter of various circles; we will find that the ration of circumference and their corresponding diameters, is always constant. This constant ratio is denoted by Greek letter . The value of is **22/7**or **3.1415**.

Or

Or (, being radius)

__Example__:

The sum of two radii of two circles is **7**cm and the difference of their circumference is **8** cm. Find the two circumferences.

__Solution__:

** **Let be the radius of one circle.

The radius of the other circle cm

Now, circumference of circle with radius cm cm --- (1)

and, circumference of circle with radius cm --- (2)

The difference of two circumference **= 8** cm --- (3)

From equations (1), (2) and (3) we get

cm

Thus, circumference of the circle with radius cm **=26** cm and circumference of second circle,

cm

__Example__:

What will be the circumference of a circle inscribed an equilateral triangle of side **9** cm.

__Solution__:

Let be the centre of the inscribed circle of

Since, radius of inscribed circle in a triangle

Now Area of

Semi perimeter of

Radius of inscribed circle cm

Circumference of the circle

cm