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

Draw a line segment AB.

(i) With A as centre and radius more than half of AB , draw arcs on both sides of AB.
(ii) With the same radius and B as centre, draw arcs cutting the arcs drawn in step (i) at P and Q.
(iii) Join P and Q. PQ intersects AB at C.
(iv) With A as centre and radius more than half of AC, draw arcs on both sides of AC.
(v) With the same radius and C as centre, draw arcs cutting the arcs drawn in step (iv) at R and S.
(vi) Join R and S. RS intersects AB at D. ​

Now, AC and CB are equal.

Both are $\frac{1}{2}$(AB).

Again, divide AC at D.

So, AD and AC are of same length, i.e., $\frac{1}{4}$(AB).