Math Doubts

Constant property of a circle

The ratio of a circle’s circumference and its diameter is always a constant.

Introduction

To start studying the circles in geometry, everyone must learn an important property firstly. The ratio of the circumference of a circle to its diameter is a constant. It can be observed by comparing the ratios of two different circles. So, let’s construct two circles with different radii geometrically.

From a point, turn the thread around circle to reach the same point. After that, cut the thread and compare the length of the thread by a ruler. Remember, the length of the thread is the circumference of that circle.

constant property of circle

You will observe that the length of the thread is equal to the $18.85 \,cm$ approximately. We know that the radius of the circle is $3 \,cm$. So, the diameter of the circle is equal to $6 \,cm$. Now, find their ratio mathematically.

$Ratio$ $\,=\,$ $\dfrac{18.85}{6}$

$\implies$ $Ratio$ $\,=\,$ $\dfrac{\cancel{18.85}}{\cancel{6}}$

$\implies$ $Ratio$ $\,=\,$ $3.1416666666\cdots$

$\,\,\,\therefore\,\,\,\,\,\,$ $Ratio$ $\,\approx\,$ $3.1417$

Repeat the same procedure for drawing another circle geometrically and calculate the ratio.

constant property of circle

In this case, the radius of the circle is $4\,cm$. So, its diameter is equal to $8\,cm$. You will observe that the circumference of the circle is $25.15\,cm$ approximately. Now, calculate the ratio of the circle’s circumference to its diameter.

$Ratio$ $\,=\,$ $\dfrac{25.15}{8}$

$\implies$ $Ratio$ $\,=\,$ $\dfrac{\cancel{25.15}}{\cancel{8}}$

$\implies$ $Ratio$ $\,=\,$ $3.14375$

$\,\,\,\therefore\,\,\,\,\,\,$ $Ratio$ $\,\approx\,$ $3.1437$

Property

Compare the ratios for understanding the constant relation between the circumference of a circle to its diameter.

  1. In the case of $3\,cm$ radius circle, the ratio of circle’s circumference and its diameter is $3.1417$
  2. In the case of $4\,cm$ radius circle, the ratio of circle’s circumference and its diameter is $3.1437$

The two ratios are approximately equal. Even, you construct another circle with a different radius, you get the same value because the ratio of the circumference of a circle to its diameter is always constant. It is called the constant property of a circle.

Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more