From unit circle to regular octagon and back

Geometry Level 4

In a unit circle, square \( ABCD \) is inscribed. A new square \( A'B'C'D' \) is constructed when the square \( ABCD \) is translated by a vector \( \vec{AB} \). Finally, an equilateral \( \triangle XYZ \) is drawn, so that rectangle \( AB'C'D \) is inscribed in it and the following is fulfilled:

  • Points \( B' \wedge C' \in XY \), \( A \in XZ \) and \( D \in YZ \).

Calculate the area of regular octagon whose side length is equal to the distance between points \( O \) and \( Z \). Give answer to 2 decimal places.

The image below represents how everything should look like when the drawing is done. Click here to enlarge the image.

Basically: Calculate the green region

Basically: Calculate the green region

If there is a question regarding the problem, it can be asked here.


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