5. Explain how a collapsing compass can be used to transfer a segment.

Solution:

7. Partition a given segment into seven congruent segments.

Solution:

8. Partition a given segment internally and externally in the ratio of 3 to 2, given a unit segment.

Solution:

12. Construct the circumcenter of a triangle.

Solution: Construct the perpendicular bisectors of two sides. The intersection is the required point.

14.Construct the incenter of a triangle.

Solution: Construct the internal bisector of two angles. The intersection is the required point.

16. Construct an excenter of a triangle.

Solution: Construct the external bisector of two angles. The intersection is the required point.

18. Construct the nine-point circle of a triangle.

Solution: The midpoints of the sides are three points on the required circle. Construct the perpendicular bisectors of two of the segments joining the midpoints. The intersection is the required center.