How do you divide a circle into three parts?

Answer 1

I assume that you want to divide it into three equal "pie slices".

If you have the location of the center of the circle, and are allowed to use a protractor (or other angle-measuring device), then you draw a radial line segment from the center to the circle, then another radial line segment at a 120° and to the first radial line segment, and final radial line segment at a further 120° angle.

If you have only the circle, a straight-edge, and a compass, then you must first locate the center of the circle. Draw two cords, Use the compass to construct bisecting perpendicular lines for each chord. These bisecting perpendicular lines will meet at the center of the circle.

If you now draw a chord equal in length to the radius, and radial lines from each of its ends, then that gives you a "pie slice" that is one sixth of the circle! So if you draw a second chord where the first ends, you have a "pie slice" that is one third of the circle.

So you could draw five chord, each the length of the radius, each starting where the previous ended, and draw radial lines through every second chord-end. Or you could use the first two chords to find the length of a chord which corresponded to a third of the circle.

(Actually, you don't really have to draw any of these chords, you just need to mark their end-points as you go along.)