How many circles can be in a set of concentric circles?
(a) 3
(b) 2
(c) 4
(d) There is no set of numbers of circles that can be in a set of concentric circles.

Question

How many circles can be in a set of concentric circles? (a) 3(b) 2(c) 4(d) There is no set of numbers of circles that can be in a set of concentric circles.

Vedantu Content Team · Accepted Answer

Hint: First look at the definition of concentric property. Look at the definition of circle. Combine both the definitions to get a combined definition of concentric circle. Now take center at origin. Try to draw circles with different radii. Check the options for the number of circles drawn one by one to rule out the wrong options. Tick the remaining options which are true for concentric circles.Complete step-by-step answer:Circles: A circle is a 2-dimensional shape consisting of all points in a place that are at a given distance from a given point, the centre. The given distance is radius. It can also be defined as the path traced by moving point under condition that it moves in such a way that its distance from one given point remains constant always. Concentric circles: Concentric circles are the circles with only one common centre. The region between two concentric circles with a different radius is called annulus. Any two circles can be made concentric by inversion by picking the inversion centre as one of the limiting points. The given option is 3, 2, 4 for being circles in a set of concentric circles. Let us assume the centre to be the point defined as origin denoted by 0. Let us draw a circle with radius 1 units, we get it as:

Let us draw a circle with radius 2 units, we get it as:

Set of two circles. Let us draw a circle with radius 3 units, we get it as:

Set of 3 circles. Let us draw with 4 units, radius, we get it as:

4 circles set. So, there is no particular number we can get any number of circles. So, the correct answer is “Option D”.Note: Generally, students confuse between set and pair. They gave it as a set of concentric, students misread it and kept 2 answers. But it is wrong. The idea of fixing a centre and drawing with different radii and thereby prove infinite circles all possible is very important to draw them carefully.