Draw a line segment AB and by ruler and compasses, obtain a line segment of length (AB).

Steps of construction:

(i) Draw a line segment AB.

(ii) Draw a circle with centre A with radius more than 1/2 AB.

Similarly, Draw a circle with centre B with same radius which intersect above circle at M and N respectively.

(iii) Draw line segment MN which intersect AB at point O.

On measuring,

AO=BO=1/2 AB

(iv) Draw a circle with centre A with radius more than 1/2 AO.

Similarly, Draw a circle with centre O with same radius which intersect above circle at P and Q respectively.

(v) Draw line segment PQ which intersect AO at X.

On measuring,

AX=XO=1/2 AO=1/4 AB

∴ XB=XO+BO=1/4 AB+1/2 AB=3/4 AB