We have to bisect the line segment of length 10 cm and again bisect the half of its original line segment

We follow the following steps for the construction

STEP1: Draw line segment AB having length 10 cm.

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.

STEP 5: 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.

STEP8: Measure the length of AN.

Length of line segment AN must be 2.5 cm