Draw a line segment `A B` and bisect it. Bisect one of the equal parts to obtain a line segment of length `1/4(A B)`

Explanation

Steps of construction :

1. Draw a line segment AB.

2. With the help of ruler and compasses, draw the bisector of AB which bisects AB at C.

3. Similarly, in the same way draw the bisector of AC at D.
We see that `AC = 1/4(AB)`.