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21994TCS: P6 - P10

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  • Antreas
    Jul 25, 2013
    • 0 Attachment
      [Hatzipolakis - F. Javier]

      Let ABC be a triangle, P = (x:y:z) a point and A'B'C'
      the pedal triangle of P.


      A* := (The Reflection of BC in BP) /\ (The Reflection of BC in CP)

      B* := (The Reflection of CA in CP) /\ (The Reflection of CA in AP)

      C* := (The Reflection of AB in AP) /\ (The Reflection of AB in BP)

      [The triangles A*BC, B*CA, C*AB share the same incenter P]

      Oa := The Circumcenter of A*BC
      Ob := The Circumcenter of B*CA
      Oc := The Circumcenter of C*AB

      P* := The Point of Concurrence of the Circumcircles
      of A*BC, B*CA, C*AB
      [We have seen recently this point in Hyacinthos]

      La := The Reflection of P*Oa in B'C'

      Lb := The Reflection of P*Ob in C'A'

      Lc := The Reflection of P*Oc in A'B'.

      The Triangles ABC, Triangle bounded by (La,Lb,Lc)
      are parallelogic for P on the Euler line.

      One of the parallelocic centers lies on the circumcircle.

      Coordinates of Parallelogic centers on the circumcircle
      for P = H, O, G, N and midpointGH in a File in the Reference: