Given the set a = {(x, y) | x | + | y | = a, a > 0}, B = {(x, y) | XY | + 1 = | x | + | y |}, if a ∩ B is a set of vertices of a regular octagon on a plane, then the value of a is Please explain why,

Given the set a = {(x, y) | x | + | y | = a, a > 0}, B = {(x, y) | XY | + 1 = | x | + | y |}, if a ∩ B is a set of vertices of a regular octagon on a plane, then the value of a is Please explain why,

The factorization of B is (| x | - 1) (| y | - 1) = 0, so | x | = 1 or | y | = 1, and its image is made. It is 4 straight lines, enclosing a square with side length of 2 and vertex (+ - 1, + - 1). For | x | + | y | = a, a > 0, its image is a square whose vertex is the origin on the coordinate axis. When the square in a contains the square in B, a intersects the straight line in B