Concentric circles - Horse
Channel: Zeewaqar Husnain
Date: 23/08/2023

In Geometry, the objects are said to be concentric when they share a common centre. Circles, spheres, regular polyhedra, regular polygons are concentric as they share the same centre point. In Euclidean Geometry, two concentric circles should have different radii from each other. In this article, you will learn what are concentric circles, the theorem on concentric circles, the region between the concentric circles, equations, and examples in detail.

Concentric Circles Meaning

The circles with a common centre are known as concentric circles and have different radii. In other words, it is defined as two or more circles that have the same centre point. The region between two concentric circles are of different radii is known as an annulus.

Concentric Circle Equations
Let the equation of the circle with centre (-g, -f) and radius √[g2+f2-c] be

x2 + y2 + 2gx + 2fy + c =0

Therefore, the equation of the circle concentric with the other circle be

x2 + y2 + 2gx + 2fy + c’ =0

It is observed that both the equations have the same centre (-g, -f), but they have different radii, where c≠ c’

Similarly, a circle with centre (h, k), and the radius is equal to r, then the equation becomes

( x – h )2 + ( y – k )2 = r2

Therefore, the equation of a circle concentric with the circle is

( x – h )2 + ( y – k )2 = r12

Where r ≠ r1

By assigning different values to the radius in the above equation, we shall get a family of circles.

https://byjus.com/maths/concentric-circles/#:~:text=Concentric%20Circles%20Meaning,is%20known%20as%20an%20annulus.