It is known from Bottema's theorem that if we have two squares with a common vertex, we can complete the formation as in the figure to make two other squares that also have a common vertex.
But I just discovered something additional: the sum of the areas of the first two squares is equal to the sum of the areas of the next two squares. In other words, we can write: $A+B=C+D$
I haven't proven it yet but I checked the equality on GeoGebra
My question is, is this feature already discovered? If there are any references you can mention, please post them
I don't think it's too hard to prove but I haven't tried it yet, don't prove it please but any hints are helpful