Circles distance II

In a cube of side 1 unit, on one face we draw a circle inscribed in that face.
On one adjacent face, we draw the circumscribed circle to that face.

Find the minimum distance between these 2 circles

The answer is an algebric number.

Answer format: the minimal polynomial for this algebric number // $\dots ,a_3,a_2,a_1,a_0$ where $P(x)=\cdots +a_3\times x^3+a_2\times x^2+a_1\times x+a_0$ is the minimal polynomial

Example: 1,-1,-1 // if the answer would be the golden ratio $\varphi$