Question

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

Answer 1

Steps of construction:

(i) Given AB bar 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 bar .

(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.

(vi) Thus PQ bar is the required line segment whose length is twice that of AB.