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simple circle


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The largest circle inscribed in a cube will be in a plane that creates a cross section of the cube in a shape of a regular hexagon. The circle will be inscribed into that hexagon. The plane is perpendicular to the largest diagonal of a cube and cuts the cube at the midpoints of its edges. The side of the hexagon is 1/sqrt(2), so the inradius is sqrt(3)/2sqrt(2).

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