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Tracks of incenter・excenter

There is a circle O and the three corners of ΔABC are on the circle.
Please find the track of the incenter when point A moves on the circle.
Do you think it is strangely?

  1. : Track of incenter
  2. : Doubt (1)
  3. : Track of excenter
  4. : Doubt (2)
  5. : Excenter are three.
  6. : Incenter and excenter are brothers

Forum of Geometric Constructor by Y.Iijima