structural:reformatting
Point in plane

For an arbitrary point in the plane of a regular hexagon with circumradius R {\displaystyle R}, whose distances to the centroid of the regular hexagon and its six vertices are L {\displaystyle L} and d i {\displaystyle d_{i}} respectively, we have

If d i {\displaystyle d_{i}} are the distances from the vertices of a regular hexagon to any point on its circumcircle, then