Problem #5

• Given a unit circle, a collection of line segments in its plane is said to be good if any (infinite) line that meets the circle also meets at least one of the segments in the collection. An example of a good collection of total length 6 is shown below.
  

  Find a good collection of line segments in the plane with the shortest total length you can.

• Given a unit sphere, a collection of line segments in space is said to be good if any (infinite) plane that meets the circle also meets at least one of the segments in the collection. An example of a good collection of total length 14 is shown below.
  

  Find a good collection of line segments in space with the shortest total length you can.

Source: A problem from the Latvian Mathematical Olympiad and its generalization

The solution will be posted shortly.

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