Theorem 5.3b: The perimeter of the quadrilateral region in the figure above is

2rcos(180k/n)sin(360/n)sec(180j/n)sec(180(j-2)/n).

proof: From Theorem 4.4a we know that

sj = rcos(180k/n)[tan(180j/n) - tan(180(j-1)/n)]

and

sj-1 = rcos(180k/n)[tan(180(j-1)/n) - tan(180(j-2)/n)]

Hence

sj + sj-1 = rcos(180k/n)[tan(180j/n) - tan(180(j-2)/n)]

which is the distance from a Pj point to a Pj-2 point, as one could see from looking at the figure. Thus, by Theorem 4.4b,

2(sj + sj-1) = 2rcos(180k/n)sin(360/n)sec(180j/n)sec(180(j-2)/n)

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