Question

given some line segment ab whose length you do not know construct PQ such that the length of PQ is twice that of AB​

Answer 1

Answer: Steps of construction:

(i) Given 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 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 PQ¯¯¯¯¯¯¯ is the required line segment whose length is twice that of AB.