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21258Re: A conic centered at Euler line

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  • Francisco Javier
    Oct 26, 2012
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      Dear friends:

      I now see that this is a particular case of some projective theorem: "the locus of poles with respect a conic of the tangents to another conic is also a conic".

      Here is the version for two circles:

      (A) and (B) are circles
      The line AB intersect (B) at M and N
      M' and N' are the inverses of M and N with respect to (A)
      J is the inverse of A with respect to (B)
      O is the inverse of J with respect to (A)
      A' is the reflection of A on O
      The locus points P such that the polar of P with respect to (A) is tangent to (B) is a conic with foci A and A' and diameter M'N'.

      what is the description of the locus in the general case in terms of the two given conics?

      Thank you.
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