Conjecture. Let Euler line of ABC intersects the sidelines at P,Q,R resp. Consider the Xn centers of triangles on their circumcircles suct that Xn center of ABC, Xn center of AQR, Xn center of BPR, Xn center of CPQ are concyclic then for any point on Neuberg cubic of ABC, Xn centers of PBC, PCA, PAB and P are concyclic. Some examples of Xn centers are: X(99), X(107), X(110), X(476).
Conjecture. Let Euler line of ABC intersects the sidelines at P,Q,R resp. Consider the Xn centers of triangles on their circumcircles suct that Xn center of ABC, Xn center of AQR, Xn center of BPR, Xn center of CPQ are concyclic then for any point on Neuberg cubic of ABC, Xn centers of PBC, PCA, PAB and P are concyclic.
ReplyDeleteSome examples of Xn centers are: X(99), X(107), X(110), X(476).