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Concentric Circle

Concentric circles are two or more circles that share the exact same center point but have different radii. Because they have the same center, they fit inside one another and never intersect.

Key Concepts

The distance between any two concentric circles remains constant and is equal to the difference between their radii.
The flat, ring-shaped region bounded by two concentric circles is known as an annulus.
In geometry, if a chord of the larger concentric circle touches the smaller circle, it acts as a tangent to the smaller circle and is bisected at the point of contact.

Formula & Equation

Areaofthering(annulus)=pi(R2āˆ’r2)Area of the ring (annulus) = pi(R^2 - r^2)

R is the radius of the larger outer circle, and r is the radius of the smaller inner circle. pi is approximately 22/7 or 3.14.

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Common Misconceptions

Myth: Concentric circles and congruent circles are the same thing.
Fact: Congruent circles have the same radius but can have different centers, meaning they can be placed anywhere. Concentric circles must have the exact same center but always have different radii.

Real World Applications

The scoring rings on an archery target or dartboard, which share a central bullseye.
The circular ripples that form and expand outward when a stone is dropped into a still pond.

Frequently Asked Questions

Do concentric circles ever intersect?
No, concentric circles never intersect because they share the same center and have different radii, keeping them at a constant distance from each other.
How do you find the area between two concentric circles?
You subtract the area of the smaller inner circle from the area of the larger outer circle using the formula pi(R^2 - r^2).

Keep Learning

CircleArea of a CircleTangent