Radius and Centre

A radius is a line segment connecting the centre of a circle or sphere to its perimeter. From the centre to any point on the circumference of the circle or sphere, the radius is the same length. It is half of the diameter’s length. In this article, we’ll learn more about radius.

Radius

The radius is a line segment that connects the centre of a circle or sphere to its perimeter or boundary in geometry. It is commonly abbreviated as ‘r’ and is an integral part of circles and spheres. The plural of radius is “radii,” which is used when discussing multiple radiuses at once. The diameter is the longest line segment in a circle or sphere connecting any points on the opposite side of the centre, while the radius is half the diameter’s length. It can be written as d/2, where d is the circle or sphere’s diameter.

Centre Radius of circle

A circle is the collection of all points in a plane that are at a fixed distance from a fixed point in the plane. The fixed point is referred to as the centre “O” in this case. A circle’s radius is an important component. It is the distance between the circle’s centre and any point on its circumference. In other terms, the radius of a circle is the straight line segment that connects the centre of a circle to any point on its perimeter. Because the circumference of a circle is infinite, it can have several radiuses. This signifies that a circle has an endless number of radii and that all of the radii are equally spaced from the circle’s centre. When the radius of the circle changes, the size of the circle changes. A circle is the collection of all points in a plane that are at a fixed distance from a fixed point in the plane. The fixed point is referred to as the centre “O” in this case.

How do you calculate the radius of a circle?

When the diameter, area, or circumference of a circle are known, the radius can be calculated using the three basic radius formulas. Let’s utilise these formulas to calculate a circle’s radius.

Radius = Diameter/ 2 is the formula when the diameter is known.

Radius = Circumference/2π is the formula when the circumference is known.

The radius is calculated using the formula Radius = ⎷(Area of the circle/π).).

For instance, if the diameter is 24 units, the radius will be 24/2 = 12 units. If a circle’s circumference is provided in units, its radius can be calculated as 44/2π.

Equation of Circle

The equation of the circle is required to represent a circle on the Cartesian plane. If we know the centre and radius of a circle, we can draw it on a piece of paper. Similarly, we can draw a circle on a Cartesian plane if we know the centre and radius coordinates. A circle can be depicted in a variety of ways:

• General form

• Standard form

• Parametric form

• Polar form

Let’s learn about the circle equation, its different forms, graphs, and solved instances in this post.

Standard Equation of a Circle

The standard equation of a circle provides exact information about the circle’s centre and radius, making it much easier to read the circle’s centre and radius at a glance. The usual equation for a circle with a radius of r and a centre at (x₁,y₁) is  (x−x₁)² + (y−y₁)² = r² where (x, y) is any point on the perimeter of the circle.

Conclusion

The beginning of the general version of the circle equation is always x² + y². When a circle crosses both axes, there are four spots where the circle and the axes overlap there are only two points of contact when a circular hits both axes. It is not the equation of the circle if any equation of the form x² + y² + axy + C =0. In the circle equation, there is no xy term. The circle equation is usually represented in polar form by the letters r and. The radius is the distance between the circle’s centre and any point on its circumference. As a result, the value of the circle’s radius is always positive.