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19635A point related to a quadrilateral

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  • jpehrmfr
    Jan 1, 2011
      Dear Hyacinthists
      with my best greetings for 2011 for you, your family and your friends, I have a little question :
      Consider a quadrilateral A_1,A_2,A_3,A_4
      For k =1,2,3,4, T_k is the triangle with vertices the A_i except A_k; O_k is the circumcenter of T_k, (O_k) the circumcircle and B_k the isogonal conjugate of A_k wrt T_k
      Then the inverse of B_k in (O_k) doesn't depend on k and this point M is the center of the homothecy mapping O_1,O_2,O_3,O_4 to B_1,B_2,B_3,B_4.
      Is there a special name for this point M? Do you know some references?
      Friendly. Jean-Pierre
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