Theorem 4.4b: In an {n/k} star inscribed in a circle of radius r, if 1 < 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 3: In the triangle OPiPj,
the side in which we are we are interested is opposite to the angle from Pj through O to Pi. This angle we have seen to be 180(j±i)/n. The side opposite to the angle at Pi is rj. The angle at Pi is 90 ± 180i/n. Let s be the distance from Pj to Pi. The Law of Sines then gives us
Hence the distance from Pj to Pi is