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Re: [EMHL] Greetings and a problem

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  • xpolakis@mac.com
    ... The circle (C1) touches A1A2 at Ca, and A3A1 at Ba The circle (C2) touches A2A3 at Ab, and A1A2 at Cb The circle (C3) touches A3A1 at Bc, and A2A3 at Ac A
    Message 1 of 2 , Jan 12, 2002
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      Stanley Rabinowitz wrote:

      >Let A1A2A3 be a triangle.
      >Inside the triangle are the 3 Malfatti circles
      >with centers C1, C2, C3. (C1 closest to A1, etc.)
      >Let A2C3 meet A3C2 at B1.
      >Let A3C1 meet A1C3 at B2.
      >Let A1C2 meet A2C1 at B3.
      >Then (conjecture) A1B1, A2B2, A3B3
      >are concurrent at a point P.

      The circle (C1) touches A1A2 at Ca, and A3A1 at Ba
      The circle (C2) touches A2A3 at Ab, and A1A2 at Cb
      The circle (C3) touches A3A1 at Bc, and A2A3 at Ac

      A' = A2Bc /\ A3Cb. Similarly B', C'.

      A" = A2Ba /\ A3Ca. Similarly B", C".

      Are the triangles A'B'C', A"B"C" in perspective with ABC?

      Antreas
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