the circle is inscribed in the polygon
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the circle is inscribed in the polygon
A square or an equilateral triangle for example when a circle is inscribed within it.
... touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are tangent to both circles.
Circumscribed.
If the tangent circles are outside of one another, then neither passes through the center of the other. If one circle is within the other, then the inner tangent circle might contain the center point of the larger circle. There will be infinitely many inner tangent circles that do not.