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