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Eight Vertices of a Octagon

Source: 1987 National High School Mathematics League, Exam One, Problem 6

February 24, 2020

Problem Statement

Set A={(x,y)∣∣x∣+∣y∣=a,a>0},B={(x,y)∣∣xy∣+1=∣x∣+∣y∣}A=\{(x,y)||x|+|y|=a,a>0\},B=\{(x,y)||xy|+1=|x|+|y|\}. If A∩BA\cap B is a set of eight vertices of a regular octagon, then a=a=________.
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