Question

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.

Answer 1

1. Draw a line segment `overline"XY"` of 12.8 cm.
   
2. Draw a circle, while taking point X as centre and radius more than half of XY. 
   
3. With same radius and taking centre as Y, again draw arcs to cut the circle at A and B. Join AB which intersects `overline"XY"` at M. 
   
4. Taking X and Y as centres, draw two circles with radius more than half of `overline"XM"`.  
   
5. With same radius and taking M as centre, draw arcs to intersect these circles at P, Q and R, S. 
   
6. Join PQ and RS. These are intersecting `overline"XY"` at T and U.
   

7. Now, `overline"XT"` = `overline"TM"` = `overline"MU"` = `overline"UY"`. These are 4 equal parts of `overline"XY"`.
   By measuring these line segments with the help of ruler, we will find that each is of 3.2 cm.