Construction of a Circle

A circle is a collection of all those point in a plane whose distance from a fixed point remains constant.

Centre: The fixed point in the plane which is equidistant from every point on the boundary of a circle is called centre.

In figure, O is the centre of the circle.

Radius: The fixed distance between the centre and any point on the boundary of the circle is called radius.

In figure, OX is a radius.

Chord: A line segment joining any two points on a circle is called a chord of the circle.

In figure, MN is a chord.

Diameter: A chord that passes through the centre of a circle is called diameter of the circle.

In figure, YZ is a diameter. The length of a diameter = 2 × radius.

In a circle, diameter is the longest chord.

Construction of a Circle when the Length of its Radius is Given:

Working Rules for Construction of a Circle:

Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be put on a mark say 3 cm (Let the radius of the circle be 3 cm).

Step II: Mark a point with pencil where we want the centre of the circle: Let it be O.

Step III: Place the pointer of the compass on O which we have marked in step II.

Step IV: Turn the compass around the point O to get the required circle.

Constructing a Circle:

We draw a circle with the help of a pair of compasses, provided in the geometry box and a fine pointed pencil.

Let us draw a circle of radius 4 cm. We observe the following steps.

Step I: We expand the two arms of a pair of compasses and take the measure of 4 cm on the scale by placing pointed end at zero and the other end having a pencil at 4 cm, mark on the scale as shown in the figure.

Step II: We take a convenient point O on a piece of paper.

Step III: We fix the pointed end of the pair of compasses at O and move the pencil point around holding the pair of compasses firmly at the top. We get the desired round shape called a circle.

Example on Construction of a Circle:

1. Draw two circle of radii 4 cm and 5 cm with same centre O.

I. Open the compass by putting the pointer on initial point of a scale and by opening the pencil-end upto 5 cm.

II. Marka point O with pencil and consider it as centre of the circle.

III. Place the pointer of the compass on O.

IV. Turn the compass around O to get the circle of radius 5 cm.

V. With the help of same above steps, draw an another circle of radius 4 cm having the same O as centre.

Solved Example on Circle:

1. Find the radius of circle whose diameter is 28 cm.

Solution:

Radius of a circle = $\frac{\textrm{Diameter of the circle}}{\textrm{2}}$ 

                         = $\frac{28}{2}$ cm

                         = 14 cm

Worksheet on Construction of a Circle:

1. Multiple Choice Questions (MCQ) on Circle:

   Tick (✔) the correct option.

(i) The radius of a circle of diameter 20 cm is

(a) 8 cm

(b) 10 cm

(c) 4.0 cm

(d) 4.5 cm

(ii) Find the diameter of the circle when radius is

(a) 3.8 cm

(b) 7.3 cm

(c) 2.9 cm

(d) 4.8 cm

(iii) O is the centre of a circle, and its radius is 5 cm. Where does P lie, when

(i) OP = 5.2 cm?

(ii) OP = 5cm?

(iii) OP = 4.8 cm?

4. Draw two circles one having radius 6 cm and other having 3 cm as shown in the following figure such that the inner circle passes through centre of the other circle.

5. Draw two circles of equal radii with centres A and B such that each one of them passes through the centre of the other. Check whether AB ⊥ CD.

6. With the same centre O, draw three circles of radii 2.5 cm, 3.5 cm and 4.5 cm.

7th Grade Math Problems 

8th Grade Math Practice 

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