Three octagons

The rectangles are 3 by 4. Which of the three bounding octagons have similar shape?

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The first and third octagon are similar, the second is not.

Solution by Lewis Corner.

Remark by Matthew Arcus: Once again, Bob Ruyle points the way to great generalities: take an isosceles triangle with height p, base 2q, then apex angle is 2α where tan α = q/p, then tan 2α = 2pq/(p²-q²), so 2α is also an angle of the Pythagorean triangle with sides p²+q²:2pq:p²-q².

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