**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.

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.

In the figure given above, C₁ and C₂ are two circles having the same center O with different radii r₁ and r₂ respectively.

Circles C₁ and C₂ 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 > r₁)

**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**₁** and C**₂** 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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