Without measuring, divide the line segment [AB] below into 3 equal segments. - Junior Cycle Mathematics - Question 14 - 2014

Label the points where the circle intersects the line segment AB. Let these intersection points be P and Q, where P is closer to A.

With the same radius used for the first circle, place the compass pointer at point P and draw an arc above and below the line segment. Repeat this from point Q. The arcs should intersect, creating two additional points above and below the line. Label these new points as R and S.

Draw straight lines from points R and S down to meet the line segment AB, creating two additional intersection points. Label these intersection points as D and E, where D is to the left of E.

Now, the line segment AB is divided into three equal segments: AD, DE, and EB.