The two important properties on circle are stated below:
1. The ratio of the circumference to the diameter of any circle is constant and the value of this constant is denoted by the Greek letter π.
Therefore, the circumference of any circle/diameter of that circle = constant = π
or, the circumference of any circle = π × diameter of that circle.
If r be the radius of the circle then its diameter is 2r.
Therefore, the circumference of the circle = π ∙ 2r = 2πr.
The constant quantity π is an incommensurable number i.e., it cannot be expressed as the ratio of two positive integers. An approximate value or π is 27/7; a more accurate value of π is 355/133 or, 3.14159 (correct to five places of decimals).
2. Angles at the center of a circle are proportional to the lengths of the arcs which subtend those angles.
The above two important properties on circle will help us to prove that a radian is a constant angle.
Click Here to know how to prove that “a radian is a constant angle”.
● Measurement of Angles