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

Q2.    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}.

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The steps of construction are followings:

(i) Given \bar{AB} whose length is not known.

(ii) Fix the compasses pointer on A and the pencil end on B. The opening of the instrument now gives the length of\bar{AB}.

(iii) Draw any line 'l'. Choose a point P on 'l'. Without changing the compasses setting, place the pointer on Q.

(iv) Draw an arc that cuts 'l'  at a point R.

(v) Now place the pointer on R and without changing the compasses setting, draw another arc that cuts 'l' at a point Q.

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

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