**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".

Apart from the stuff given above, if you want to know more about "Concentric-circles", please click here

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**