Tuesday, December 4

What to understand by diameter of a circle


What is a circle?
In a third grader’s language, a circle is a closed figure with curved side or no sides. A circle is defined by its centre and its radius. The centre of a circle is the point exactly in the middle of the circle such that every point on the circle is at the same distance from the centre of the circle. The radius of the circle is the distance between the centre of the circle and any point on the circle. Since all points on a circle are at the same distance from the centre of the circle, there can be infinitely many radii (plural of radius) of a circle.

What is the diameter of a circle?
When we draw two radii from the centre of a circle to any two different points on a circle, an angle is formed such that the two radii are the rays of the angle. This angle can be an acute angle, an obtuse angle, a right angle, a straight angle or also a reflex angle. When this angle is a straight angle, that is, when the angle at the centre subtended by the two radii is 180 degrees, the two radii form a straight line that passes through the centre of the circle and touches two points on the circle. Such a line is called the diameter of the circle. In other words, a diameter of a circle is a line that passes through the centre of the circle and touches any two points on the circle as well.

Diameter of a circle can also be defined in terms of the chord of a circle. A chord of a circle is a line segment that joins any two points on the circle. If a chord is such that it passes through the centre of the circle then it is called the diameter of the circle.
Just as in radii, a circle can have infinitely many diameters as well. By the definition of a diameter stated above, we also see that all the diameters would pass through the centre of the circle. Therefore we can say that all diameters of a circle are concentric.

How to find the diameter of a circle?
From the definition of a diameter above we saw that the length of the diameter would be two times that of the radius. Therefore the diameter of a circle formula can be written like this:
d = 2r
Where, d  is the diameter of the circle and r is the radius of the circle.

No comments:

Post a Comment

Post a Comment