Friday, June 24, 2022

1873. A Family Of Conics Centered at X(5)-NPC center

 Lat ABC be an acute angled triangle and P be a point.

A1B1C1-cevian triangle of P and A2B2C2-circumcevian triangle of P.
Oba=Circumcenter of (BA1A2),  Oca=Circumcenter of (CA1A2).
Circle through the points A2,Oba, Oca intersects the BC at A3, A4.
Define B3,B4,C3,C4 cyclically.

*A3, A4, B3, B4, C3, C4 lie on same conic. For all P, center of conic is X(5)-NPC center.
Are there any remarkable properties of perspectors of these family of conics?

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