Question

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"`. 

Answer 1

The following steps will be followed to construct a line segment ­`overline"PQ"`  such that the length of `overline"PQ"` is twice that of `overline"AB"`. 

1. Let `overline"AB"` be the given line segment.
   
2. Adjust the compasses up to the length of `overline"AB"`.
   
3. Draw any line l 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 l at point Q.   
   
   `overline"PQ"` is the required line segment.