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Q.2 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 :

I : Draw \(\overline{AB} \)of any suitable length.
II : Place the needle of the compass at A and the other pencil end at B.
III : Draw a line l and take a point P on it.
IV: With the same opening of the compass, place the needle at P and mark another point Q on l.
Thus \(\overline{PQ} \) is the required line segment
whose length is twice the length of \(\overline{AB} \) i.e \(\overline{PQ} \) = 2\(\overline{AB} \) .

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