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

Here is the reson why the two yellow colored angle are equal . The two red line are parallel and the black colored line is crossing both so the two yellow angle are equal.