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

Hint: Here we will proceed by fixing the compass on one point and pencil on another point such that it will give the unknown length of the line segment. Then drawing another line, where we will choose a point and with the same fixation of compass, we will place a pointer on Q. Then repeat this step, to get the required result.

Complete step-by-step answer:
Steps of construction-

Given $\overline {AB} $ whose length is not known.


Fix the compasses pointer on A and the pencil end on B. The opening of the instrument now gives the length of $\overline {AB} $.

Draw another line ‘l’. Choose a point on ‘l’. Without changing the compasses setting, place the pointer on Q.


Draw an arc that cuts ‘l’ at the point R.



Now place the pointer on R and without changing the compasses setting draw an arc that cuts ‘l’ at point P.


Thus $\overline {PQ} $is the required line segment whose length is twice that of AB.

Note: In order to solve this question, we must focus that while making the arc, the compass opening should be the same at every point to get the accurate result. Also we must be careful that points taken on line segments should be as per given conditions.