Theorem 4.4a: In an {n/k} star inscribed in a circle of radius r, if 0 < i < j < n/2 then the distance from the Pj points to the Pi points on a line of the star is

If the points are on the same side of Po use the minus sign. If they are on opposite sides, use the plus sign.

proof: In the figure in the proof of the previous result,

 

we see that the distance from the Po point to the point is rcos(180k/n)tan(180j/n). It follows that the distance from the Pj points to the Pi points is rcos(180k/n)[tan(180j/n) ± tan(180i/n)] depending on whether the points are on the same side of Po or not.

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