ADGEOM 1387

 

[Tran Quang Hung]:

Dear geometers,

Let ABC be a triangle with incircle (I). D,E,F are midpoints of BC,CA,AB, reps.

(Ka) is circle passing through E,F and touch (I) at X and (Ka) is different than NPC.
(Kb) is circle passing through F,D and touch (I) at Y and (Kb) is different than NPC.
(Kc) is circle passing through D,E and touch (I) at Z and (Kc) is different than NPC.

Then AX,BY,CZ are concurrent at a point on (I).

Could you please help me, Is this point known ?

Thank you and best regards

Tran Quang Hung.

 

[César Lozada]:

 

Dear Tran Quang Hung:

The point is X(1358).

Regards

César Lozada