How to divide a given line into four equal parts

Question :
Divide line AB, 9 cm long, into four equal parts.


Answer :
Step by step construction given below

Draw line AB 9 cm long.


Point A as the centre and radius slightly larger than half of AB, draw two arcs on both the sides of the line AB.


Now point B as the centre and the same radius, draw arcs intersecting the former ones in points  P and Q.


Draw line PQ intersecting line AB in point O.
Line AB divide it into two equal parts AO and OB.


Point A as the centre and radius slightly larger than half of AO, draw two arcs on both the sides of the line AO.


Now point O as the centre and the same radius, draw arcs intersecting the former ones in points R and S.


Draw line RS intersecting line AO in point C.
Line AO divide it into two equal parts AC and CO.


Point B as the centre and radius slightly larger than half of OB, draw two arcs on both the sides of the line OB.

Point O as the centre and the same radius, draw arcs intersecting the former ones in points T and U.

Draw line TU intersecting line OB and name the bisecting point as D.

Thus, the three points C, O and D divide line AB into four equal parts.

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