Q

# 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 $\overline{AB}$.

Views

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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