Is it zero? Part II

Geometry Level 3

Let there be a natural number $a$ , such that $a \gt 2$ . Then, let there be $a$ non-overlapping circles, such that all the circle's centers (the points) are collinear.

What is the minimum number of straight lines which can be drawn, which are guaranteed to be tangential to all $a$ circles?

Notes:

Three or more points are collinear if they all lie on a single straight line.
Unlike Part I , the circles here are not necessarily unit circles.

2 Infinite 4 1 0 3

1 solution

Richard Desper
May 17, 2019

It is simple enough to find an example with $a = 3$ where no such lines could possibly exist. Draw three circles along the $x$ -axis, with centers $(0,0), (2,0)$ , and $(10,0)$ . Let the radii of these circles be $1$ , $10^{-15}$ , and $1$ respectively. No line tangent to the first two circles will be tangent to the third.

Is it zero? Part II

1 solution

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