# Relation Between the Circumference and Diameter

It we measure the circumference and diameter of various circles, we will find that the ratio of the circumference and their corresponding diameters is always constant. This constant ratio is denoted by the 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 circumferences is **8**cm. Find the two circumferences.

__Solution__:

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

The radius of the other circle is cm

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

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

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

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

cm

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

cm

__Example__:

Find the circumference of a circle inscribed in an equilateral triangle of side **9** cm.

__Solution__:

Let be the centre of the inscribed circle of

Since the radius of the inscribed circle in a triangle

Now the area of

Semi perimeter of

Radius of inscribed circle cm

Circumference of the circle

cm