Post-less combination window & door system
As to whether it is geometrically feasible, I have no idea.  The question you should be asking is whether it is structurally feasible. I doubt there is any conceivable way to get a header that turns 120° and would provide enough support in the corner without a post there.  I'm assuming that the dashed line is an existing wall. I would also evaluate whether or not the wall is load bearing - based on the floor plan, it looks like it might need to have a header as well.

I would consult with an engineer or an architect before progressing with floor plans.