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