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22057Fwd: Locus problems

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  • Antreas Hatzipolakis
    Mar 18, 2014
    • 0 Attachment


      ---------- Forwarded message ----------
      From: Antreas Hatzipolakis 
      Date: Mon, Mar 17, 2014 at 11:46 PM
      Subject: Locus problems
      To: anopolis@yahoogroups.com


      Let ABC be a triangle and A'B'C' the cevian triangle of P = O.

      The circle (O, OA') intersects again BC at A", the circle
      (O,OB') the CA at B" and the circle (O,OC') the AB at C".

      1. The parallels through A",B",C" to AA', BB', CC' resp.
      concur at H.

      2. The triangles ABC and orthic triangle of A"B"C" are perspective (??)

      In general, which is the locus of P such that:

      1. The parallels through A",B",C" to AA',BB',CC', resp.
      are concurrent? (also I is on the locus)

      2. The triangles ABC and orthic triangle of A"B"C" are perspective?

      APH