CONCENTRIC 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 above.

The above figure represents two concentric circles and the area between the two concentric circles is shaded in red color.

The red colored area is known as circular ring.

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

where r₂ > r₁.

Construction of Concentric Circles

Example :

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.

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 C₁ and C₂ are drawn.

Width of the circular ring = OB – OA

= 5 – 3

= 2 cm

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