# CONCENTRIC CIRCLES

Concentric circles :

In this section, we are going to learn about Concentric circles.

Already we are familiar with Circles.

When a small stone was dropped in still water, you might have seen circular ripples were formed. Which is the center of these circles ?

Is it not the place where the stone was dropped ?

Yes.

The circles with different measures of radii and with the same center are called concentric-circles. The center is known as common center.

## The Concentric-circles

Circles drawn in a plane with a common center and different radii are called concentric-circles. See the figure given below.

Look at the following two figures :

The above figure represents two concentric-circles.

In the above figure, the area between the two concentric -circles are shaded with red color.

The red colored area is known as circular ring.

## Description - Circular ring

In the figure given above, C  and C are two circles having the same center O with different radii r and r₂  respectively.

Circles C and C are called concentric-circles.

The area bounded between the two circles is known as circular ring.

Width of the circular ring  =  OB – OA =  r₂  - r₁ ( r₂  > r)

## Construction of concentric circles

Question :

Draw concentric-circles with radii 3 cm and 5 cm and shade the circular ring.

Find its width.

Solution :

Given: The radii are 3 cm and 5 cm.

Steps for construction :

Step 1 :

Draw a rough diagram and mark the given measurements.

Step 2 :

Take any point O and mark it as the center.

Step 3 :

With O as center and draw a circle of radius OA = 3 cm

Step 4 :

With O as center and draw a circle of radius OB = 5 cm.

Thus the concentric-circles C and C are drawn.

Width of the circular ring  =  OB – OA

Width of the circular ring  =  5 – 3

Width of the circular ring  =  2 cm.

After having gone through the stuff given above, we hope that the students would have understood "Concentric-circles".

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