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Concentric Circles: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Concentric CirclesConcentric Circles: Definition and ExamplesTable of ContentsConcentric Circles Definition of Concentric Circles

Concentric circles are two or more circles that share the same center point but have different radii. A circle is a two-dimensional geometric figure defined as the collection of all points equidistant from a fixed point called the center, with that fixed distance being the radius. When you draw multiple circles with the same center but different sizes, you create concentric circles. It's important to note that circles with different centers cannot be concentric.

The region formed between two concentric circles is known as an annulus, which resembles a flat ring or donut shape. The area of this annulus can be calculated using the formula A=π(R2−r2)A = \pi(R^2 - r^2)A=π(R2−r2), where RRR is the radius of the outer circle and rrr is the radius of the inner circle. Concentric circles appear in many real-life situations such as dartboards, ripples in water, and wheels of ships.

Examples of Concentric Circles Example 1: Finding the Width of an Annulus Problem:

Find the width of the annulus if the radius of the bigger circle is 8 feet and the radius of the smaller circle is 5 feet.

Step-by-step solution:

Step 1, Write down what we know. The radius of the bigger circle (R) = 8 feet and the radius of the smaller circle (r) = 5 feet.

Step 2, Calculate the width of the annulus. The width equals the difference between the two radii:

Width = R - r = 8 - 5 = 3 feet Example 2: Finding the Radius of the Smaller Circle Problem:

If the width of annulus is 7 inches and the radius of the bigger circle is 12 inches, then what is the radius of the smaller circle?

Step-by-step solution:

Step 1, Write down what we know. The radius of the bigger circle (R) = 12 inches and the width of the annulus = 7 inches.

Step 2, Calculate the radius of the smaller circle. Since the width equals the difference between the two radii, we can write:

Radius of the smaller circle (r) = R - width = 12 - 7 = 5 inches Example 3: Finding the Area of an Annulus Problem:

Find the area of the annular region between the concentric circles with radii 333 and 555 units.

Finding the Area of an Annulus

Step-by-step solution:

Step 1, Identify what we have. The radius of outer circle (RRR) = 555 units and the radius of inner circle (rrr) = 333 units.

Step 2, Use the formula for the area of an annulus:

Area = π(R2−r2)\pi(R^2 - r^2)π(R2−r2).

Step 3, Substitute the values into the formula:

Area = 227×(52−32)\frac{22}{7} \times (5^2 - 3^2)722​×(52−32)

Step 4, Calculate the values inside the parentheses:

Area = 227×(25−9)\frac{22}{7} \times (25 - 9)722​×(25−9)

Step 5, Simplify further:

Area = 227×16\frac{22}{7} \times 16722​×16

Step 6, Calculate the final answer:

Area = 50.2850.2850.28 square feet Comments(1)NNatureLover75September 17, 2025I’ve used the concentric circles definition and examples from this page to help my kids understand geometry better. The step-by-step explanations made it so easy to explain concepts like annulus area!

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