Where did you get such nonsense?
If you scaled the figure up or down, the relationship would go away; that implies angles are irrelevant.
The numbers used are very special; if the circumference is 1 more than the diameter, then the latter must satisfy the equation \(\pi d = d + 1\), whose solution is \(d = \frac{1}{\pi-1} = 0.46694220692425985998339481323367\).
So the relationship has nothing to do with the figure (especially the inscribed right angle), but entirely with the particular number used.