Dear Greg and Alex,

I just have generalized (and it is easy) the result as following:

n >=3 is one integer.
X1, Y1, X2, Y2, X3, Y3, ... Xn, Yn are any 2n points concyclic on one circle O with diameter W
y1, y2, y3, ... yn are distances from Y1, Y2, Y3, ... Yn to X1X2, X2X3, X3X4, ... XnX1 respectively.
x1, x2, x3, ... xn are distances from X1, X2, X3, ... Xn to YnY1, Y1Y2, Y2Y3, ... Yn-1Yn respectively.
a1, a2, a3, ... a2n are sides of polygon X1Y1X2Y2X3Y3 ... XnYn (by this order). It means:
a1 = X1Y1
a2 = Y1X2
a3 = X2Y2
a4 = Y2X3
...
a(2n-1) = XnYn
a2n = YnX1
We can use the same my posted proof to prove the following result:

a1*a2*a3* ... *a2n = x1*x2*x3* ... *xn*W^n = y1*y2*y3* ... *yn*W^n

Best regrads,
Bui Quang Tuan