Step by Step Methods to Draw a Perfect Circle Using Compass and Without Compass
You all play with a ball. What is the shape of the ball? Is it circular or something else? Yes, right, it’s circular. What is this circle? A circle is a closed, curved object with two dimensions in geometry. A circle is a sphere with no edges or bounds. A circle is also known as the location of points that are evenly spaced apart from the centre. In this article, we will learn to draw a circle and understand what things are needed to draw a circle.
A Circle
Examples of Circular Shape
A car tire, a time-telling wall clock, and a lollipop are a few objects in our immediate environment that have a circular form.
Circular Shapes
Parts of Circle and Things to Draw in a Circle
The Radius of a Circle: The circle's radius is a segment of a line having one terminus in the centre and the other on the circle.
The Diameter of a Circle: The diameter of a circle is defined as the length of a line segment with its endpoints on the circle and passing through its centre.
Circumference: The distance encircling a circle is its circumference. The perimeter of other forms is the same.
Circles' Chords: The chord of the circle is a line segment whose endpoints are on a circle. A circle's largest chord is its diameter.
Arc of a Circle: An arc is a section of a circle, with all of its points falling within the circle. It has a curvature that runs the length of it. A semicircle is an arc measuring 180° that connects the diameter's endpoints.
The Secant of a Circle: A line that precisely intersects a circle at two places is said to be its secant.
Tangent of a Circle: A line that precisely crosses a circle at one point is said to be a tangent.
Circle Segments: A circle's chord divides the circular area into two sections. The term "circular segment" refers to each component.
Sector of a Circle is a circular region with an arc serving as one of its boundaries and two radii enclosing it.
Parts of a Circle
How to Draw a Circle?
We use an instrument to draw circles. This instrument is known as a compass. Two legs make up a compass. Its legs are long on one and short on the other. The pointed end of the lengthy leg resembles a needle. A pencil can be inserted into the little pipe-like holder on the short leg. By pulling apart the compass's two legs and setting the distance between the pencil tip and needle end to equal the circle's radius, you may use it to draw circles (say 2 cm). So, drawing a circle is an easy process.
Compass
Circle Needle
How to Draw a Radius?
Example:
Create a circle with a 2.5 cm radius.
Step 1: Determine the radius or diameter of the circle at the specified value.
r = 2.5 cm
D = 5 cm
$r = \dfrac{D}{2}$
$= \dfrac{5}{2}$
= 2.5 cm
Step 2: Determine the radius from the expression if the diameter is known. The compass arms should be adjusted to the circle's radius. Turn the pencil arm 360 degrees on the paper while the needle is positioned in the circle's centre. You'll receive the circle with the specified radius.
Radius
How to Draw a Circle Without a Compass?
Any circular object will serve to draw a circle. A round glass, the base of a candle, a pair of bangles, or a circle of paper can all be used. Make certain the rounded edge is only smooth.
Solved Examples
Q 1. What is the length of a circle's longest chord if its radius is 3 cm?
Ans: The circle's diameter is represented by its longest chord.
Diameter $=2 \times$ radius
$=2 \times 3$
$=6 \mathrm{~cm}$
Q 2. A circular clock's minute hand measures 14 cm in length. How far does the tip travel in one hour?
Ans: The length travelled in a single hour equals the circle-shaped clock's circumference.
$\text { Circumference }=2 \pi r$
$= 2 \times \dfrac{22}{7} \times 14$
$=2 \times 22 \times 2$
$= 88cm$
Practice Problem
Q 1. Sandra marked 2 points on a sheet of paper. She is trying to figure out the number of circles that could be constructed which will pass through the given two points. Find out the answer.
Ans: Sandra can get infinite circles passing through the given two points.
Q 2. What is the circumference of a semi-circle if its diameter is 14 units?
Ans: 35.99 units
Summary
A circle is formed by every point in a plane that is at least a certain distance from the centre, also known as the circumference. To put it another way, it is the curve that a moving point in a plane draws to maintain a constant distance from another point. The distance between any point on a circle and its centre is known as the radius. The three main qualities to remember are the circumference, which is the distance around the item. The diameter would be the length of a circle taken from one end to the other and passes through its centre, and the radius, which is equal to half of the diameter.
FAQs on How To Draw A Perfect Circle in Maths
1. How do you draw a perfect circle?
The most accurate way to draw a perfect circle is by using a compass. A compass keeps the distance from the center to the edge constant, which is the key property of a circle.
- Mark a fixed point as the center.
- Set the compass width to the desired radius.
- Place the compass needle on the center point.
- Rotate the pencil 360° around the center to form the circle.
2. What is the mathematical definition of a circle?
A circle is the set of all points in a plane that are at a fixed distance from a given point called the center. The fixed distance is known as the radius.
- If the center is (0, 0) and the radius is r, every point (x, y) on the circle satisfies:
x² + y² = r²
This definition explains why keeping a constant radius is essential when drawing a perfect circle.3. What is the formula for a circle in coordinate geometry?
The standard equation of a circle with center (h, k) and radius r is (x − h)² + (y − k)² = r². This formula represents all points that are exactly r units from (h, k).
- Center = (h, k)
- Radius = r
4. How can you draw a perfect circle without a compass?
You can draw a near-perfect circle without a compass by using a string and pencil method. This method still maintains a constant radius.
- Fix one end of a string at the center point.
- Tie a pencil to the other end.
- Keep the string tight.
- Move the pencil around the center in a full rotation.
5. What is the difference between radius and diameter in a circle?
The radius is the distance from the center to the circle’s edge, while the diameter is twice the radius and passes through the center. The relationship is:
- Diameter = 2 × Radius
- Radius = Diameter ÷ 2
6. Why does a compass draw a perfect circle?
A compass draws a perfect circle because it keeps the radius constant while rotating around a fixed center. By definition, a circle is formed when all boundary points are the same distance from the center.
- The needle fixes the center.
- The pencil maintains a fixed radius.
- The rotation traces all equidistant points.
7. How do you draw a circle given its diameter?
To draw a circle given its diameter, first find the radius by dividing the diameter by 2. The formula is Radius = Diameter ÷ 2.
- Measure the diameter.
- Divide it by 2 to get the radius.
- Mark the midpoint as the center.
- Use a compass set to the radius to draw the circle.
8. How do you calculate the area of a circle?
The area of a circle is calculated using the formula A = πr², where r is the radius. This formula measures the space inside the circle.
- Square the radius.
- Multiply by π (approximately 3.14).
9. How do you calculate the circumference of a circle?
The circumference of a circle is given by C = 2πr or C = πd. It represents the total distance around the circle.
- Use radius: C = 2 × π × r
- Use diameter: C = π × d
10. What are common mistakes when drawing a perfect circle?
Common mistakes when drawing a perfect circle include changing the radius or shifting the center point. These errors break the geometric definition of a circle.
- Not keeping the compass width fixed.
- Moving the center point accidentally.
- Letting the string become loose (in string method).
- Tilting the compass while rotating.
