Right Triangles and an Octagon
Source:
June 8, 2009
Problem Statement
A regular octagon is to be formed by cutting equal isosceles right triangles from the corners of a square. If the square has sides of one unit, the leg of each of the triangles has length:
(A)\ \frac{2 \plus{} \sqrt{2}}{3} \qquad
(B)\ \frac{2 \minus{} \sqrt{2}}{2}\qquad
(C)\ \frac{1 \plus{} \sqrt{2}}{2}\qquad
(D)\ \frac{1 \plus{} \sqrt{2}}{3}\qquad
(E)\ \frac{2 \minus{} \sqrt{2}}{3}