Define concentric circles.
The Correct Answer and Explanation is :
Concentric Circles Definition:
Concentric circles are two or more circles that share the same center point but have different radii. The term “concentric” comes from the Latin word “concentus,” meaning “to have the same center.” This means that the centers of all the circles coincide with each other.
Explanation:
Concentric circles are a geometric concept that involves a set of circles lying in the same plane and having a common center. The key characteristic of concentric circles is that although their radii (the distances from the center to any point on the circle) may vary, the center of all the circles remains constant. These circles can range from very small to very large, with each one nested inside the next.
The concept of concentric circles can be applied to various real-world situations. For example, in target practice, the bullseye and surrounding rings form concentric circles. Another example is the ripples created when a stone is thrown into water—the circles expand outward but share the same center at the point of impact. In architecture, concentric circle patterns can be found in the design of circular staircases or domes.
Mathematically, concentric circles can be represented in a coordinate plane. If one circle has a radius of ( r_1 ) and is centered at the origin (0,0), its equation would be:
[
x^2 + y^2 = r_1^2
]
Similarly, if another circle has a radius of ( r_2 ) (where ( r_2 \neq r_1 )), the equation for that circle would be:
[
x^2 + y^2 = r_2^2
]
Both circles share the same center (0,0), demonstrating their concentric nature. As the radii change, the size of each circle increases or decreases, but the center point remains fixed.
Concentric circles are also significant in physics and engineering, as they are used in wave propagation, especially in optics and sound waves.