In previous term we have learnt to find the area and the circumference of a circle. Now we can learn more about circles.
1. circles 2. Construction of circles 3. The Concentric Circles 4. Construction of Concentric Circles

**Construction of circles and concentric circles**

In previous term we have learnt to find the area and the circumference of a circle. Now we can learn more about circles.

** **

__1. circles__

The collection of all the points in a
plane, which are at a fixed distance from a fixed point in the plane, is called
a circle.

The fixed point is called the centre
of the circle and the fixed distance is called the radius of the circle. The word
radius is used in two senses – in the sense of a line segment which joins the centre
of the circle and a point on the circle and in the sense of length of the line segment.

A circle groups all points in the plane
on which it lies into three categories. They are: (i) the points which are inside
the circle, which is also called the interior of the circle; (ii) the points on
the circle and (iii) the points outside the circle, which is also called the exterior
of the circle.

If two points on a circle are joined
by a line segment, then the line segment is called a chord of the circle. Since
there are many points on the circles, any number of chords can be drawn in a circle.

The chord, which passes through the centre
of the circle, is called a diameter of the circle.

As in the case of radius, the word ‘diameter’
is also used in two senses, that is, as a line segment and also as its length.

It can be easily verified that the diameter is the longest chord and all diameters have the same length. The diameter is equal to two times the radius.

** **

__2. Construction of circles__

Now let us learn to construct circle
with given radius and diameter.

**Example**** **Construct
a circle of radius 5* cm *with centre O.

**Step 1: **Mark a point O on the paper.

**Step 2: **Extend the compass distance equal to
the radius 5 *cm*

**Step 3: **At center O, Hold the compass firmly
and place the** **pointed end of the compass.

**Step 4: **Slowly rotate the compass
around to get the circle.

** **

__3. The Concentric Circles__

Circles drawn in a plane with a common
centre and different radii are called ** concentric
circles **(

The area between the two concentric circles
is known as ** circular ring** (

Width of the circular ring (see *Fig.
4.21*)

= OB – OA= r_{2} − r_{1}.

** **

__4. Construction of Concentric Circles__

**Example **Draw concentric circles with
radii 4* cm *and 6* cm *and shade the
circular ring. Find its width.

**Step 1: **Draw a rough diagram and mark the given
measurements.

**Step 2: **Take any point O and mark it as the centre.

**Step 3: **With O as centre and draw a circle of
radius OA = 4 *cm*

**Step 4: **With O as centre and draw a circle of
radius OB = 6 *cm*.

Thus the concentric circles C_{1}
and C_{2} are drawn.

Width of the circular ring = OB – OA
= 6 – 4 = 2 *cm*.

Tags : Geometry | Term 3 Chapter 4 | 7th Maths , 7th Maths : Term 3 Unit 4 : Geometry

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7th Maths : Term 3 Unit 4 : Geometry : Construction of circles and concentric circles | Geometry | Term 3 Chapter 4 | 7th Maths

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