I am very curious, if it is possible to invert the Japanese Theorem. So, if the middlepoints of the inner circle create a rectangle, is the quadrilateral on the outside of the four circles always a cyclic quadrilaterals?
I searched for hours in the web but found nothing. And after trying a lot of different ideas to proof it, I want to ask for help now. I am convinced, that it is invertable, because I wasn't able to find a exeption by using GeoGebra. Have anyboy an idea, how to solve this problem?