## Concentric circles

### Concentric circles are circles that share the same center point

Concentric circles are circles that share the same center point. In other words, they have the same central point but different radii. This means that all points on one circle are equidistant from the center of the other circle(s) within the set.

To visualize concentric circles, you can imagine a target board. The outermost circle represents the largest circle with the bullseye as its center. As you move inward, each subsequent circle represents a smaller circle, still with the same center. The bullseye itself is also a circle. In this example, the circles are said to be concentric, as they have the same central point.

Mathematically, we can define a concentric circle by using the distance formula. Let (h, k) be the center coordinates of the circles, and let r1 and r2 be the radii of the two concentric circles.

The equation for a circle with center (h, k) and radius r1 is given by: (x – h)^2 + (y – k)^2 = r1^2

Similarly, the equation for the other concentric circle with the same center (h, k) but radius r2 is given by: (x – h)^2 + (y – k)^2 = r2^2

These two equations describe the set of points on the respective circles, with the center (h, k) being the common point.

Concentric circles can be found in various real-life applications, such as dartboards, ripples in water caused by a droplet, or the layers of an onion. They are also frequently used in geometry problems and construction designs.

##### More Answers:

Exploring Three-Dimensional Shapes | A Guide to Understanding Solids and Their PropertiesExploring Polyhedra | Shapes, Faces, Edges, and Vertices in Three-Dimensional Geometry

Understanding the Key Concepts of Circles | Radius, Diameter, and Circumference