A regular Polygon of an even number of sides being inscribed in a circle as ABC...A'...C'B'A' so that AA' is a diameter if two angular points next but one to each other as B, B' be joined, and the other lines parallel to BB' and joining pairs of angular points be drawn as CC', DD',...., then

(BB' + CC' +.... ) / AA' = A'B / BA

Similarly, the these traingles are euqal and the ratio of the side of traingles are equal .

so BF/FA = B'F/FK = CG/GK = C'G/GL = ............

=E'I / IA'

Summing the antecedents and consequents respectively , we have

(BB'+ CC'+ ..................)/ AA' = BF/FA = A'B / BA