By Tom Kantain | Updated Aug 30, 2022
In classical geometry, bisecting lines, angles, and circles is straightforward with a compass and straightedge. Trisecting an arbitrary angle, however, is impossible using only those tools. Trisecting a circle, on the other hand, is a simple exercise that can be completed with the same instruments.
Using the compass as a straightedge, draw a straight line that passes through the circle’s center. Label the center “C” and the two points where the diameter meets the circle’s circumference “A” and “B.”
Place the compass point at B and the pencil tip at C, adjusting the compass so that its radius equals the circle’s radius. Draw an arc centered at B that cuts the circle on both sides. Mark these intersection points “D” and “E.”
Draw straight lines from C to D and from C to E. The rays CA, CD, and CE divide the circle into three congruent sectors. This works because points D and E lie exactly one‑sixth of the circle’s circumference from B, which is one‑half of the circle away from A.
