How to Divide a Circle Into Thirds
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.
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Instructions
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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.
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Label this line segment "AB."
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Draw two circles of equal size using your compass, one with a center on "A," and the other with the center on "B." Make the radii of these circles at least 1/2 of the length of "AB," so that your two new circles intersect.
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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.
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Erase the two new circles, but leave the line segments.
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Draw two new circles of equal size using your compass, one with a center on "C," and the other with the center on "D." Make the radii of these circles at least 1/2 of the length of "CD" so that your two new circles intersect.
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Draw another line segment using your ruler across the intersection of the two new circles. You can call this line segment "EF."
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Notice where the line segment "EF" bisects the line segment "CD." This is the center of your circle.
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Place a protractor so that the base runs along either the "EF" or "CD" line segment and the origin is on the center of your circle.
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Measure a 120 degree angle by locating the zero degree and 120 degree points on the protractor and marking these points on your circle.
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Draw lines from the center of the circle through the marks you made up to the edge of the circle.
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Place your protractor so that the origin is on the center of your circle and the base runs along one of the new lines you just made.
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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.
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Draw lines from the center 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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References
- Photo Credit protractor image by timur1970 from Fotolia.com
