Is it zero?
Let there be a natural number , such that . Then, let there be non-overlapping unit circles, such that all the circle's centers (the points) are collinear.
How many straight lines can be drawn, such that each line is tangential to all circles?
Note: Three or more points are collinear if they all lie on a single straight line.
(Part II of the problem is here )
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1 solution
Since all the circles have the same radius, we may draw two lines parallel to the line through the centers of the circle, one on each side of said line, with each line a constant distance of 1 from the original line. Each of these two lines will be tangent to each circle exactly once.
No other line will be tangent to more than two circles.