What are Concentric Circles? Meaning, Diagram & Formula

The concept of concentric circles plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding concentric circles helps students distinguish between different types of circles and solve geometry problems easily.

What Is Concentric Circles?

Concentric circles are circles that have the same center point but different radii. In simple words, two or more circles are called concentric if they share one common center but their sizes (radii) are not equal. You’ll find this concept applied in topics such as area of a circle, types of circles, and geometry theorems.

Key Formula for Concentric Circles

Here’s the standard formula to calculate the area between two concentric circles: \( \text{Area} = \pi (R^2 - r^2) \), where R is the radius of the bigger circle and r is the radius of the smaller circle.

Properties of Concentric Circles

• All concentric circles have the same center point.
• Each circle has a different radius.
• They do not cross each other (except at the common center).
• The distance between any two concentric circles is the difference of their radii.
• The region between two concentric circles is called an annulus.

Step-by-Step Illustration

1. Use a compass to draw a circle with center O and radius r (smallest circle).
2. From the same center O, draw another circle but with a larger radius R.
3. Now you have two (or more) circles centered at O but with different sizes. These are concentric circles.

Concentric Circles Diagram

Imagine a "bullseye" or target pattern often seen in dart boards or archery targets. Each ring is a concentric circle drawn from the same central point, but with increasing radii.

Example Problem: Area Between Concentric Circles

Question: Find the area between two concentric circles if the radius of the larger circle is 10 cm and the smaller circle is 6 cm.

Solution:

1. Area of larger circle = π × 10² = 100π

2. Area of smaller circle = π × 6² = 36π

3. Area between them = 100π − 36π = 64π

4. Using π ≈ 3.14, Area = 64 × 3.14 = 200.96 cm²

Cross-Disciplinary Usage

Concentric circles are not only useful in Maths but also play an important role in Physics (such as sound and water ripples), Computer Science (target diagrams for data structures), and daily logical reasoning. Students preparing for exams like JEE or NEET will see this concept often, especially in geometry and measurement problems.

Real-Life Examples of Concentric Circles

• Dartboards and archery targets (bullseye patterns)
• Ripples formed when a stone is dropped in water
• Cross-sections of tree trunks showing growth rings
• Radar screens showing distance rings from a central point
• Artworks, such as those by artist Wassily Kandinsky

Concentric Circles vs Eccentric and Congruent Circles

Type	Common Center?	Same Radius?	Description
Concentric	Yes	No	Circles share one center, but each has different radius.
Congruent	Not necessary	Yes	Circles have equal radii, centers can differ.
Eccentric	No	Can be any	Circles do not share the same center.

Try These Yourself

• Draw three concentric circles with radii 2 cm, 4 cm, and 6 cm using a compass.
• Find the area between two concentric circles with radii 8 cm and 5 cm (take π = 3.14).
• List two real-life objects that show a pattern of concentric circles.
• Explain the difference between concentric and congruent circles in your own words.

Frequent Errors and Misunderstandings

• Confusing concentric circles with congruent circles (same center vs. same radius).
• Forgetting to square the radii when using area formulas.
• Mixing up the larger and smaller radius in area calculations.

Relation to Other Concepts

The idea of concentric circles connects with topics such as parts of a circle (like center and radius), difference between concentric and congruent circles, and area of an annulus. Mastering concentric circles helps students tackle advanced geometry and measurement tasks.

Classroom Tip

A quick way to remember concentric circles is to think about the rings inside a tree trunk or the shape of a target board. Vedantu’s teachers often share these visual cues in live classes for easy memory and better understanding.

We explored concentric circles—from definition, properties, formulas, real-life examples, common errors, and links to similar mathematical ideas. Keep practicing problems and participating in Vedantu’s interactive sessions to quickly solve exam questions on concentric circles with confidence!

Useful Internal Links

• Area of a Circle
• Parts of Circle
• Circle Theorem
• Annulus (Area Between Circles)