How to divide a given line into eight equal parts

Question :
Divide line AB, 7 cm long, into four equal parts.


Answer :
Step by step construction given below

Draw line AB 7 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.


Point B as the centre and the same radius, draw arcs intersecting the former ones in points I  and J.


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


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



With point O as the centre and the same radius, draw arcs intersecting the former ones in points K and L.


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


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


With point B as the centre and the same radius, draw arcs intersecting the former ones in points M and N.


Draw line MN intersecting line OB in point D.
Line OB divide it into two equal parts OD and DB.


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


Point C as the centre and the same radius, draw arcs intersecting the former ones in points P and Q.


Draw line PQ


Line PQ intersecting line AC in point E.
Line AC divide it into two equal parts AE and EC.


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


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 CO in point F.
Line CO divide it into two equal parts CF and FO.


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



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



Draw line TU intersecting line OD in point G.
Line OD divide it into two equal parts OG and GD.


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



Point B as the centre and the same radius, draw arcs intersecting the former ones in points V and W.



Draw line VW intersecting line DB in point H.
Line DB divide it into two equal parts DH and HB.

Thus, the seven points E, C, F, O, G, D and H divide line AB into eight equal parts.

Line AB has been divided into eight equal parts.

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