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Difference of given segments

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See also the animated version.

After doing this Your work should look like this

Start with two given segments a and b.

1.  Mark a point P towards the left of the work area.
2.  Draw a long line from P to the right.
3.  Set the compasses width to the length of the segment a.

(Note: We can use the given segments in any order.)
4.  Without changing the compass width, place the point on P and make an arc across the line, creating point Q
5.  Set the compasses width to the length of the segment b.
6.  Without changing the compass width, place the point on Q and make an arc across the line to its left.
Done. The segment PR has a length which is the difference between the lengths of a and b
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Non-Euclidean constructions