How to Divide a Circle Into Thirds

Written by christina sloane
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In many geometry courses, you will be expected to divide a circle equally into thirds. Since a circle is 360 degrees, you might know that a circle can be split up into three equal, 120 degree parts. If you have a compass, protractor and ruler, it is easy to measure and draw three equal portions to satisfy this assignment.

Skill level:
Easy

• Paper
• Pencil
• Compass
• Ruler

Instructions

1. 1

Draw a straight line segment (also called a chord) using your ruler inside your circle, so that each end touches an edge of the circle.

2. 2

Label this line segment "AB."

3. 3

Draw two circles of equal size using your compass, one with a centre on "A," and the other with the centre on "B." Make the radii of these circles at least 1/2 of the length of "AB," so that your two new circles intersect.

4. 4

Draw a line segment "CD" across the intersection of the two new circles using your ruler, extending it to the edge of your original circle.

5. 5

Erase the two new circles, but leave the line segments.

6. 6

Draw two new circles of equal size using your compass, one with a centre on "C," and the other with the centre on "D." Make the radii of these circles at least 1/2 of the length of "CD" so that your two new circles intersect.

7. 7

Draw another line segment using your ruler across the intersection of the two new circles. You can call this line segment "EF."

8. 8

Notice where the line segment "EF" bisects the line segment "CD." This is the centre of your circle.

9. 9

Place a protractor so that the base runs along either the "EF" or "CD" line segment and the origin is on the centre of your circle.

10. 10

Measure a 120 degree angle by locating the zero degree and 120 degree points on the protractor and marking these points on your circle.

11. 11

Draw lines from the centre of the circle through the marks you made up to the edge of the circle.

12. 12

Place your protractor so that the origin is on the centre of your circle and the base runs along one of the new lines you just made.

13. 13

Measure a second 120 degree angle by locating the zero degree and 120 degree points on the protractor and marking these points on your circle.

14. 14

Draw lines from the centre of the circle through the marks you made up to the edge of the circle. Now the circle is sectioned into three equal parts.

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