​ Given some line segment AB, whose length you do not know, construct PQ such that ​

Question

Given some line segment \(\over{AB}\), whose length you do not know, construct \(\over{PQ}\) such that the length of \(\over{PQ}\) is twice that of \(\over{AB}\).

The following steps will be followed to construct a line segment \(\over{PQ}\) such that the length of \(\over{PQ}\) is twice that of \(\over{AB}\).

Answer 1

(1) Let \(\over{AB}\) be the given line segment.

(2) Adjust the compasses up to the length of \(\over{AB}\)

(3) Draw any line 1 and mark a point P on it.

(4) Put the pointer on P and without changing the setting of compasses, draw an arc to cut the line segment at point X.

(5) Now, put the pointer on point X and again draw an arc with the same radius as before, to cut the line 1 at point Q.

\(\over{PQ}\) is the required line segment.