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22501Radical Center - OI line

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  • Antreas Hatzipolakis
    Jul 6 4:15 PM
      I was wondering which triads of circles of a triangle,
      if reflected in the respective angle bisectors, have radical
      center lying on the OI line.

      1. Let (Ma), (Mb), Mc) the circles with diameters BC,CA,AB,
      resp. and (M'a), (M'b), (M'c) their reflections in AI,BI, CI, resp.
      The radical center of (M'a), (M'b), (M'c) is the reflection of O in I.

      2. Let (Na), (Nb), (Nc) be the NPCs of IBC,ICA,IAB, resp.
      and (N'a), (N'b), (N'c) their reflections in AI,BI,CI, resp.
       I think that the radical center of (N'a), (N'b), (N'c) is
      lying on the OI line (and probably I have posted it before!)

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