ADGEOM 1458 * ADGEOM 1459

[Tran Quang Hung]:

 

Dear Geometers,

Let ABC be a triangle with excircles (Ia),(Ib),(Ic). Then

Polars of I with respect to (Ia),(Ib),(Ic) bound a triangle that is perspective with ABC.

Polars of H with respect to (Ia),(Ib),(Ic) bound a triangle that is perspective with ABC.

Please help me find perspectors in ETC and which is the points P have this property ?

Best regards,

Tran Quang Hung.

 

 

[Nikos Dergiades]:

 

Dear Tran Quang Hung,

this question has been answered by Jean-Pierre.

See at K033 Spieker Central Cubic of Bernard Gibert katalogue

where he writes

 

locus of point M such that the polar lines of M in the three excircles bound a triangle perspective to ABC (together with the line at infinity and the radical circle of the excircles) (Jean-Pierre Ehrmann, Hyacinthos #9605)

Best regards

 

Nikos Dergiades