An Alternative to Euclid's Collapsing Compass Construction:

Given : Segment AB and Point C

Construct : A segment onto Point C congruent to Segment AB

1. Construct a Ray starting at Point B and that goes through the random Point C.

2. Construct at circle with center at Point B and circumference through Point A.

This will create a new point D.

3. Construct a circle with center at the new point D and circumference through Point B.

This will create a new point E.

5. Construct the midpoint of Segment EF. (The construction for the midpoint has not been shown here to avoid clutter.)

Result : Segment GC will be congruent the original given Segment AB.