Question

Draw a line segment AB and bisect it. Bisect one of the equal parts to obtain a line segment of length $\frac{1}{2}$ (AB)

Answer 1

We are asked to draw a line segment of any length, bisect it and again bisect it such that it is equals to

We will follow certain algorithm to construct the figure

Steps of construction

STEP1: Draw line segment AB of any length.

STEP2: With centre A and radius greater than half of AB, draw two arcs one on each side of AB.

STEP3: With centre B and taking same radius, draw two arcs one on each side of AB, intersecting the previous two arcs at C and D respectively.

STEP4: Draw a line segment having end-points C and D. Segment CD is the perpendicular bisector of AB. Let CD intersects AB at M.

STEP5: With centre A and radius greater than half of AM, draw two arcs one on each side of AM.

STEP6: With centre M and taking same radius, draw two arcs one on each side of AM, intersecting the previous two arcs at E and F respectively.

STEP7: Draw a line segment having end-points E and F. Segment EF is the perpendicular bisector of AM. Let EF intersects AM at N.

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Disclaimer: In the question, instead of $\frac{1}{2}\left(AB\right)$, there should be $\frac{1}{4}\left(AB\right)$.