In Geometry, the objects are said to be concentric if they share a common center. Circles, spheres, regular polyhedra, regular polygons are concentric as they share the same center point. In Euclidean Geometry, two circles that are concentric have the same center but always have different radii.
|1.||What Are Concentric Circles?|
|2.||Concentric Circle Examples in Real Life|
|3.||Annulus: The Region Between Concentric Circles|
|4.||Solved Examples on Concentric Circles|
|5.||Practice Questions on Concentric Circles|
|6.||FAQs on Concentric Circles|
What Are Concentric Circles?
Concentric circles are circles with the same or common center. In other words, if two or more circles have the same center point, they are termed as concentric circles. The following figure shows two concentric circles with the same center O.
Concentric Circle Examples In Real Life
Have you ever observed the wheel of a ship? It has two concentric circles joined by the spokes. Many of us have played darts. A dartboard also has concentric circles. The circles in the dartboard are drawn around a common center, that is, the bull's eye.
Annulus: The Region Between Concentric Circles
The area/region formed between two concentric circles is called an annulus. It is flat-shaped like a ring. The area of the annulus can be calculated by finding the area of the outer circle and the inner circle. We need to find the difference between the areas of both circles to get the result. The shaded part in the following figure shows the annulus.
Observe the following figure. We can find the area of the annulus (the blue region) by subtracting the area of the smaller circle from that of the larger circle. The radius of the small circle is denoted by 'r' and the radius of the large circle is denoted by 'R'. So, in order to find the area of the annulus, we can use the formula: (πR)2 - (πr)2 = π (R2 - r2)
- Concentric circles always have the same center.
- The radius of two concentric circles is equal if both the circles lie on each other.
- The annulus is the region bounded by two concentric circles.
Topics Related to Concentric Circles
Example 1: Determine if the figures given below represent concentric circles.
Concentric circles have a common center point, which is the most important property defining concentric circles. Thus, we can say that both (a) and (b) represent concentric circles.
Example 2: The diameter of two concentric circles are 14 inches and 36 inches, respectively. Determine the annulus for these concentric circles.
The radius of the inner circle is: r = 14/2 inches = 7 inches. The radius of the outer circle is: R = 36/2 = 18 inches. The annulus is calculated by the formula π(R2-r2).
Therefore, Annulus= π(R2-r2) = (22/7) × (182-72) = (22/7) × (324 - 49) = (22/7) × 275 = 864.28 inches2.
Example 3: A race track is in the form of a ring. The inner radius of the field is 58 inches and the outer radius is 63 inches. Find the area of the race track.
Given that, R = 63 inches and r = 56 inches. Let the area of the outer circle be A1 and the area of the inner circle be A2. The area of the race track is calculated as: A1 - A2 = π(R)2 - π(r)2 = π (632 -562) = (22/7) × 833 = 2618 inches2
Therefore, the area of the race-track = 2618 inches2
FAQs on Concentric Circles
What is Annulus?
The area bounded by two concentric circles is called an annulus. In other words, the path between two concentric circles is known as the annulus.
How Many Points Are Shared by Concentric Circles?
Concentric circles share no common points. They just have a common center.
What Are Concentric and Congruent Circles?
Two or more circles that have the same center, but different radii are known as concentric circles. Two or more circles with the same radius, but different centers are known as congruent circles.
How To Draw Concentric Circles?
Concentric circles can be drawn by using a compass. First, draw the circle with the smaller radius, then keeping the same center, draw the circle with the bigger radius.
How to Find the Area of the Annulus?
The area of the annulus can be calculated by finding the difference between the area of the outer circle and the inner circle. The formula used to calculate the area of the annulus is π(R2-r2); where 'R' is the radius of the outer circle and 'r' is the radius of the inner circle.