Whether you're cutting into a pizza or you're working on a craft project, it can be helpful to know how to split a circle into equal segments.
Unlike polygons, circles don't have any straight sides, which means that you can't use a ruler to accurately measure a circle without having first done a few calculations.
Once you've worked out how to split a circle into equal halves and quarters, the process for dividing circles into smaller segments becomes easier.
In this guide, we'll look at how you can perfectly divide any circle into segments using only a few simple tools.
To divide a circle equally, you first need to find its centre point.
This is easy to do if you have drawn the circle using a compass or string as you will have made a mark in the centre to draw the surrounding edge. From this point, you can draw a straight line horizontally across the circle or a line across it to split the circle into two equal segments.
To divide the circle into more segments, it's helpful to label the lines that you have already made. Label the centre of the circle 'A'. Next, you should label the point at which one end of the line meets the edge of the circle with 'B'. The other end of the line should be labeled 'C'.
At this stage, you will need to take your compass and place one end on point C. Open the compass so that the angle is greater than one-half of the circle. Use the compass and a pencil to draw an arc across the circle making sure that the ends of the line exceed the edge of the circle on both sides. Mirror this action by placing one end of the compass onto point B, making sure to keep the same compass extension. The two arcs that you have made should overlap each other on the outside of the circle.
You will need to take a ruler and place it across the circle so that the ruler passes through the points where the two arcs meet. Draw a line across the circle making sure to keep to the ruler so that the line is straight. The line that you have drawn has divided the circle into two equal segments. This new line should be at a 90-degree angle to the first line that you drew.
The first point of the new line can be labeled 'D' and the end of the same line can be labeled 'E'. You can divide the circle into smaller segments by repeating the same steps as before, but instead placing the compass on point D, followed by point E and so on. You only need to do this step for one side of the circle as you can follow the line across to divide the opposite segment into smaller sections.
You can continue dividing the circle into as many segments as you like. Make sure that you use a ruler so that each line is straight. Each line will also need to pass through the centre point so that you can ensure each segment is equal in size.
To find the centre of a circle, you first need to draw a horizontal chord across the circle, near its edge. Next, draw a perpendicular line halfway through the chord. This second line should be drawn past where you think the centre of the circle will be. Draw another vertical line near the edge of the circle and draw a perpendicular line to it, halfway along the line. You can repeat this with another chord and a perpendicular line if you need to.
The point at which all of the perpendicular lines meet is the centre of the circle. You can repeat this process for circles of any size if you are unsure of where the centre is.
There are certain areas of a circle that are essential to calculating a circle's measurements. Below is a list of the key parts of a circle and how they can be used to calculate other measurements of a circle.
Circumference
The circumference is the perimeter of a circle. It is the total length of the circle's boundary if the circle was split and laid out in a straight line. As a circle is a round closed figure, all its boundary points are equidistant from the fixed centre point of the circle.
Knowing the circumference of a circle can help you calculate the radius, as it is the length of the diameter divided by two.
Diameter
The diameter is the widest part of a circle. It passes directly through the centre of a circle, while the two endpoints lie on the circle's circumference. The diameter is the longest chord of any circle and is double the length of the circle's radius. Diameter is written as 'd' when used in a formula.
Radius
The radius is the length between the centre of the circle and the edge (circumference) of the circle. The length will remain the same everywhere in the circle, no matter which points on the circumference you draw the line. Radius is written as 'r' when it is featured in formulas. It can also be written as d/2, where 'd' is the diameter of the circle.
Knowing the radius of a circle means that you can calculate the diameter, as it is the length of the radius multiplied by two.
Chord of a circle
The chord of a circle is a straight line that runs between two points on the circumference of a circle. The two points are also connected by the curve of the circle's edge. You can calculate the length of the chord by using the length of the radius and the angle of the connecting lines at the circle's centre.
The formula to calculate the length of a chord is: 2 × √(r2 − d2), where 'r' is the radius and 'd' is the perpendicular distance from the centre of the circle to the chord.
You can also use trigonometry to calculate the length of a chord. To do this, you should use the formula: 2 × r × sin(θ/2) where 'r' is the radius and 'θ' is the angle that is subtended at the centre of the circle. A subtended angle is created by two chords that meet at the same point on the circumference of a circle. To calculate a subtended angle, you can multiply the angle that has been made by the two joined points by two. For example, if the angle subtended at a point on the circumference is 50 degrees, the angle that is subtended by the same arc at the centre is 100 degrees.
Unlike polygons, you cannot find the circumference of a circle by using a ruler as it doesn't have any straight sides. To calculate the circumference, you need to know the radius or diameter of the circle and the value of pi. Pi (written as π) has an approximate value of 3.14 or π = 22/7. It is the ratio of circumference to diameter, which means that you can calculate the circumference of a circle if you already know the diameter (or radius as you can multiply it by two to find the diameter).
The formula to calculate the circumference of a circle is C = 2πr or C = πd where π is taken as 3.14. For example, if the radius of the circle was 25cm, the equation would be:
C = 2 × π × 25
C = 2 × 3.14 × 25 = 157cm
The circumference of the circle would therefore be 157 centimeters.
The Earth has a diameter of 12,742km. To work out the planet's circumference, the equation is as follows:
C = π x 12,742km = 40,030km
Therefore, the Earth has a circumference of 40,030km.
As previously mentioned, the radius of a circle is half the length of the circle's diameter, which means that you can calculate the radius by dividing the circle's circumference by two. However, you can also calculate the radius of a circle by using the circle's circumference. You can use the formula circumference/2π to work out the radius of a circle. For example, if a circle's circumference is 44 units, the equation would be:
44/2π
(44×7)/(2×22) = 7 units
This means that the radius of this particular circle is 7 units.
If you know the area of the circle, you can use the formula⎷(Area of the circle/π) to find the circle's radius. For example, if the area of the circle is 616 square units, the equation would be as follows:
⎷(616×7)/22 =⎷28×7 =⎷196 = 14 units
The radius of the circle with an area of 616 square units is therefore 14 units.
The area for a circle can be calculated by using the formula A = πr2 if you know the radius of the circle. For example, if a circle has a radius of 3cm, the equation would be as follows:
π × 32
3.14 x (3 x 3) = 28.26
Therefore, the area of this particular circle is 28.26 cm2.
Dividing a circle is relatively easy, as long as you have the right tools. It's essential to have a compass and a ruler if you want to divide a circle into neat and equal segments by drawing it yourself. The first step to dividing a circle is to find its centre point and split it in two with a straight line.
You can then use your compass to draw two arcs through your circle. The point at which the arcs overlap will act as a guideline for you to draw further straight lines and to divide the circle into more segments.
Circles don't have any straight sides which means that you cannot measure them with a ruler to find out how long they are. Luckily, there are formulas that you can use to find a circle's circumference, radius and area. These formulas can be used in everyday life and for scientific research, such as measuring the Earth's circumference or how large a cake is.
