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
$i.\ $Given $\overline{AB}$ 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 $\overline{AB}$.
$iii.\ $Draw any line $l$. Choose a point $P$ on $l$. Without changing the compasses setting, place the pointer on $P$.
$iv.\ $Strike an arc that cuts $l$ at a point, say, $X$.
$v.\ $Now fix the compasses pointer on $X$. Strike an arc away from $P$ that cuts $l$ at a point, say, $Q$. Now the length of $\overline{PQ}$ is twice that of $\overline{AB}$.
$ii.\ $Fix the compasses pointer on $A$ and the pencil end on $B$. The opening of the instrument now gives the length of $\overline{AB}$.
$iii.\ $Draw any line $l$. Choose a point $P$ on $l$. Without changing the compasses setting, place the pointer on $P$.
$iv.\ $Strike an arc that cuts $l$ at a point, say, $X$.
$v.\ $Now fix the compasses pointer on $X$. Strike an arc away from $P$ that cuts $l$ at a point, say, $Q$. Now the length of $\overline{PQ}$ is twice that of $\overline{AB}$.
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