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Re: [EMHL] Euler line of the pedal triangle of I.

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  • Alexey.A.Zaslavsky
    ... Dear Deoclecio! If A1, B1, C1 are are the tangent points of BC, CA, AB with the incircle, A2, B2, C2 --- the intersection points of the incircle with the
    Message 1 of 3 , Jan 22, 2004
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      >>
      >> >Let I the incenter and O the circumcenter of the triangle ABC.
      >Prove
      >> >that the circumcenter O is on the Euler line of the Pedal triangle
      >of
      >> >the I.
      >>

      Dear Deoclecio!
      If A1, B1, C1 are are the tangent points of BC, CA, AB with the incircle,
      A2, B2, C2 --- the intersection points of the incircle with the altitudes of
      A1B1C1, then the triangles ABC and A2B2C2 are homothetic and the incenter of
      A2B2C2 is the orthocenter of A1B1C1.
      So this orthocenter is in OI.

      Sincerely Alexey
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