18.73 A regular octagon is formed by cutting off equal isosceles right triangles from the corners of a square. If the side length of the square is 1, then the length of the legs of these triangles is 
(A) $\frac{2+\sqrt{2}}{3}$.
(B) $\frac{2-\sqrt{2}}{2}$.
(C) $\frac{1+\sqrt{2}}{2}$.
(D) $\frac{1+\sqrt{2}}{3}$.
(E) $\frac{2-\sqrt{2}}{3}$.
(8th American High School Mathematics Examination, 1957)
[Solution] Let the length of one leg of the cut-off isosceles right triangle be $x$, then the length of the base is $\sqrt{2} x$.
Then
$$
x+\sqrt{2} x+x=1 .
$$

We get
$$
x=\frac{2-\sqrt{2}}{2} \text {. }
$$

Therefore, the answer is $(B)$.