Concentric Circles

In Geometry, the objects are said to be concentric if they share a common center. Circles, spheres, regular polyhedra, regular polygons are concentric as they share the same center point. In Euclidean Geometry, two circles that are concentric have the same center but always have different radii.

What Are Concentric Circles?

Concentric circles are circles with the same or common center. In other words, if two or more circles have the same center point, they are termed as concentric circles. The following figure shows two concentric circles with the same center O.

Concentric Circle Examples In Real Life

Have you ever observed the wheel of a ship? It has two concentric circles joined by the spokes. Many of us have played darts. A dartboard also has concentric circles. The circles in the dartboard are drawn around a common center, that is, the bull's eye.

Annulus: The Region Between Concentric Circles

The area/region formed between two concentric circles is called an annulus. It is flat-shaped like a ring. The area of the annulus can be calculated by finding the area of the outer circle and the inner circle. We need to find the difference between the areas of both circles to get the result. The shaded part in the following figure shows the annulus.

Observe the following figure. We can find the area of the annulus (the blue region) by subtracting the area of the smaller circle from that of the larger circle. The radius of the small circle is denoted by 'r' and the radius of the large circle is denoted by 'R'. So, in order to find the area of the annulus, we can use the formula: (πR)² - (πr)² = π (R² - r²)

Important Notes

• Concentric circles always have the same center.
• The radius of two concentric circles is equal if both the circles lie on each other.
• The annulus is the region bounded by two concentric circles.