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horizon
[huh-rahy-zuh n]
noun

• the line or circle that forms the apparent boundary between earth and sky.
• Astronomy.
  
  • the small circle of the celestial sphere whose plane is tangent to the earth at the position of a given observer, or the plane of such a circle (sensible horizon).
  • Also called rational horizon.the great circle of the celestial sphere whose plane passes through the center of the earth and is parallel to the sensible horizon of a given position, or the plane of such a circle (celestial horizon).the limit or range of perception, knowledge, or the like.

• Usually horizons.the scope of a person's interest, education, understanding, etc.:His horizons were narrow.
• Geology.a thin, distinctive stratum useful for stratigraphic correlation.
• Also called soil horizon.any of the series of distinctive layers found in a vertical cross section of any well-developed soil.

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Oh, you were not talking about a line, but a line segment.
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So you don't think that a tangent has anything to do with a radius, either, correct?
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And since line segments (as you would say) have no radius, therefore tangents are impossible in our small world.
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That is, a world of very narrow horizons (aka scope of interest).
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