The two squares shown share the same center O and have sides of length 1. The length of AB is 43/99 and the area of octagon ABCDEFGH is m/n, where m and n are relatively prime positive integers. Find m+n.
[asy]
real alpha = 25;
pair W=dir(225), X=dir(315), Y=dir(45), Z=dir(135), O=origin;
pair w=dir(alpha)*W, x=dir(alpha)*X, y=dir(alpha)*Y, z=dir(alpha)*Z;
draw(W--X--Y--Z--cycle^^w--x--y--z--cycle);
pair A=intersectionpoint(Y--Z, y--z),
C=intersectionpoint(Y--X, y--x),
E=intersectionpoint(W--X, w--x),
G=intersectionpoint(W--Z, w--z),
B=intersectionpoint(Y--Z, y--x),
D=intersectionpoint(Y--X, w--x),
F=intersectionpoint(W--X, w--z),
H=intersectionpoint(W--Z, y--z);
dot(O);
label("O", O, SE);
label("A", A, dir(O--A));
label("B", B, dir(O--B));
label("C", C, dir(O--C));
label("D", D, dir(O--D));
label("E", E, dir(O--E));
label("F", F, dir(O--F));
label("G", G, dir(O--G));
label("H", H, dir(O--H));[/asy] geometryperimeterAMCAIMEnumber theoryrelatively primeAIME I