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20784[EMHL] Re: perspective centers

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  • Antreas
    Feb 1 11:55 PM
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      2012/2/1 Alexey Zaslavsky <zasl@...>


      > Let A_0, B_0, C_0 be the midpoints of sides BC, CA, AB; P be
      > an arbitrary
      > point on the Euler line of triangle ABC and A_1, B_1, C_1 be the
      > projections
      > of circumcenter O to AP, BP, CP. Then A_0A_1, B_0B_1, C_0C_1 concur.

      Is this true as well?

      Let ABC be a triangle AoBoCo the medial triangle, P a point
      on the Euler line and A1,B1,C1 the orth. projections of O on
      PAo, PBo, PCo resp.

      The triangles ABC, A1B1C1 are perspective (?).

      Locus Problem:

      Let P be a variable point. Which is the locus of P such that
      ABC, A1B1C1 are perspective?

      Is it Euler Line + Something_Else ?

      APH
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