to inradius that the height-to-width ratio of a regular hexagon is 1:1.1547005; that is, a hexagon with a long diagonal of 1.0000000 will have a distance of 0.8660254 or cos(30°) between parallel sides.

Point in plane

For an arbitrary point in the plane of a regular hexagon with circumradius , whose distances to the centroid of the regular hexagon and its six vertices are and respectively, we have

:
:
:

If are the distances from

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