Question:
Draw a line segment AB bisect it. Bisect one of the equal parts to obtain a line segment of length (1/4) (AB).
Solution:
Steps of construction:
1. Draw a line segment AB.
2. With A as center and radius more than half of AB draw arcs, one on each side of AB.
3. With B as the center and same radius draw arcs cutting the previous arcs at points P and Q respectively.
4. Join P and Q which intersects AB at C.
5. With A as center and radius more than half of AC draw arcs, one on each side of AC.
6. With C as the center and same radius draw arcs cutting the previous arcs at R and S respectively.
7. Join points R and S which intersects AC at D.
Therefore AD = (1/4)(AB)
