Concentric Circles: Definition, Examples, Two Concentric Circles

Concentric Circles refer to the figure having more than two circles with the same centre or origin. There are various figures in geometry that can be concentric but here we will study circles.

In this article, we will provide you with all the details on the meaning, properties, equation as well as some examples that will shed light on concentric circles.

Concentric Circles Examples

Coming to the concentric circles definition, these refer to circles having different radius but with the same centre or origin. There are a lot of real-life concentric circle examples therefore you don’t have to imagine them.

Some concentric circle examples have been provided below:

Concentric Circle Equations

We know that the equation of circle with centre (-g, -f) and radius √[g²+f²-c] is x² + y² + 2gx + 2fy + c =0.

So, the equation of concentric circle is:

x² + y² + 2gx + 2fy + c’ = 0

Here we observe that both the equations have the same centre, but have different radii and c ≠ c’.

Similarly, a circle with centre (h, k), and the radius r, will have the equation:

( x – h )² + ( y – k )²= r²

Hence, the circle concentric with the other circle has equation as:

( x – h )² + ( y – k )²= r₁²

Here r ≠ r₁

Quick Note: If you wish to obtain the family of circles, all you have to do is assign different values of radius.

What Is An Example Of Concentric Circles?

Example 1: Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

Solution: We are given 2 concentric circles C1 and C2 with centre O and a chord AB of the larger circle C1 which touches the smaller circle C2 at the point P. Here we need to prove that AP = BP. Let us join OP. Then, AB is a tangent to C2 at P and OP is its radius.

We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact. So, OP ⊥ AB.

Now AB is a chord of the circle C1 and OP ⊥ AB. Therefore, OP is the bisector of the chord AB, as the perpendicular from the centre bisects the chord, i.e., AP = BP.

FAQs On Concentric Circles

Now let us look at some questions that are searched on the topic:

Q: What is the concentric circle definition?
A: Concentric circles have different radius but the same centre point.

Q: What is an example of concentric circles?
A: An example of concentric circles is the shapes in the trunk of a tree, ripples in water when a stone is dropped when you cut an onion you can see concentric rings.

Q: What is the formula of concentric circle?
A: The equation or formula is ( x – h )² + ( y – k )²= r₁². We have provided a detailed explanation and proof in the article.

Q: What are concentric and congruent circles?
A: Concentric circles have different radius but same centre, on the other hand congruent circles have the same radius but different center.

That was all on concentric circles. We hope the information provided on this page helps you. However, if you have further questions feel to use the comments section and we will get back to you at the earliest. For more such informative articles, keep visiting Embibe.