Practical Geometry

Construction of Circles

Out of all the geometric shapes and figures, the circle is most commonly present around us. May it be a pizza or the coin and yes the ball that you play with are all circular in shape. Have you ever thought about how many sides a circle has or about the radius of a circle? Let us also see how to construct a circle.

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What is a Circle?

circle is a shape where all points have the same distance from the centre. Few real-world examples include a wheel, dining plate, coin etc. Drawing it properly isn’t easy with a running hand. The availability of a compass (a geometric tool) is preferred by most people, be it at school or at the workplace.

Radius of a Circle

The wheel is an example of the circle. We can see here is that every point on the circle is at the same distance from the centre. This is the basic property of the circle.

How do we draw a Circle?

Radius of a Circle

Suppose you want to draw a circle of radius 3 cm. Before that, do you know what is a radius of a circle? Well, the distance from the middle or centre of a circle towards any point on it is a radius of a circle. As we want to draw the circle of radius 3m, each point on the circle should be at the distance of 3 cm from the centre. Let start with it. Now take a ruler and a compass.

Radius of a Circle

In order to construct a circle, measure the distance as 3cm on the ruler. How do make that measurement? Keep one end of the compass at 0 and change the angle of the compass and keep the second hand of the compass at 3 cm. So now the distance between the two hands s nothing but 3cm. Now take the compass, place it anywhere on the sheet and just rotate the compass.

The point where you place the compass becomes the centre of the circle. The very important thing when you draw the circle is that do not alter the width of the compass. Keep the angle same and just rotate the compass on the sheet. You get the centre and radius of the circle. So every point on the circle is at the distance of 3cm from the centre. So we have drawn the circle with radius 3 cm.

One More Example

Let us now draw two circles with centre C, with radius 4 cm and  2.5 cm respectively.

  1. Assume that there is just one centre that is the centre C.
  2. Again we take a rule and a compass.
  3. Now measure 4 cm on the ruler and draw with the same 4 cm radius of a circle.
  4. So one circle is drawn.
  5. Now for the second circle, again measure the length of 5cm on the ruler and using the same radius draw another circle.
  6. So the second radius drawn has a  radius of 2.5 cm
  7. Both the circles have a common centre that is O.

Circles with Equal Radii

Let us draw two circles having the same radius.

Radius of a Circle

  1. We need to draw the circle in such a way that each one of them passes through the centre of the other.
  2. From the above figure, let us name the first circle as A and second circle as B
  3. So we can see that the circle A passes through point B and circle B passes through point A.
  4. For the first circle A we have taken any convenient radius
  5. Now for the second circle B, keep one hand one hand of the compass anywhere on the circle and another hand at the centre of circle A and draw another circle.

Solved Example For You

Question 1.What is the maximum number of regions into which a chord will divide a circle?

  1. 1
  2. 2
  3. 3
  4. 4

Answer : 2. The maximum number of regions into which a chord will divide a circle is 2, as AB is the chord which divides the circle into two regions.

Radius of a Circle

Question 2: How can one calculate the radius of a circle?

Answer: In order to calculate the radius of a circle, one must take the circumference and divide it by 2 times π. If a circle has a circumference of 15, one would have to divide 15 by 2 times 3.14. Afterwards, one must round the decimal point to the derived answer of approximately 2.39.

Question 3:  Can we say that radius is half of a circle?

Answer: The centre of a circle happens to be the midpoint of its diameter. That is, it divides the diameter into two equal parts; each of these parts is a radius of the circle. The radius, as such, is half the diameter.

Question 4:  Explain the formula for the circumference of a circle?

Answer: The formula for the circumference of a circle is pi multiplied by the diameter of the circle. So, one must divide the circumference by π in order to find the diameter. The diameter is referred to as the radius times two.

Question 5: What is the circumference of a circle which has 4 radius?

Answer: The diameter of a circle which has 4 radius will be 8. So, the circumference will be pi*4= 3.14*8= 25.12.

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