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Concentric Circles

Concentric circles are a system where one small circle is placed within the area of a larger circle. In the Euclidean plane, concentric circles must have different radii from each other to maintain their concentric form. However, circles in 3D may be concentric and have the same radius as each other, while at the same time being different circles. For example, two meridians of a terrestrial globe are concentric with one another as well as with the globe of the earth. In simple terms, every two great circles on a sphere are concentric with one another as well as with the sphere.

By Euler’s theorem on the distance between the circumcenter and incenter of a triangle, two concentric circles, under the condition that distance is zero, are the circumcircle and incircle of a triangle. This is only if the radius of one circle is twice the radius of the other, and in that case, the triangle is equilateral. 

The region of the plane in between two concentric circles is known as an annulus, and in the case of a sphere, the analogous region of space between two concentric spheres is called a spherical shell.

The ripples formed when a small object is dropped into still water form an expanding system of concentric circles. Another form that is commonly seen is the evenly spaced circles on the targets used in archery practice or similar sports. A coaxial cable is an electrical cable where the neutral and earth core completely surrounds the live core. This can be considered a 3-way form of concentric cylindrical shells. 

They can also be found in diopter sights. These are mechanic sights that are generally found on target rifles. They feature a large disk with a hole having a small diameter near the shooter’s eye, and a front globe sight called the tunnel. When correctly aligned, the point of impact will be right in the middle of the front sight circle.

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