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Hidden world

hidden world Cyclic and tangential polygons
Hexagons

What properties do the angles have here?
Please enable Java for an interactive construction (with Cinderella).
Clearly, the yellow hexagon is a cyclic hexagon.
Please enable Java for an interactive construction (with Cinderella). Please enable Java for an interactive construction (with Cinderella).
Please enable Java for an interactive construction (with Cinderella).