MathDB

The two squares shown share the same center

O

and have sides of length 1. The length of

\overline{AB}

43/99

and the area of octagon

ABCDEFGH

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]

Problem Statement