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14.4

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 14.4 concurrency related to NPC centers

Source:

6/7/2020
Two triangles ABCABC and PQRPQR have the same circumcircles. Let Ea,Eb,EcE_a, E_b, E_c be the centers of the Euler circles of triangles PBC,QCA,RABPBC, QCA, RAB. Assume that dad_a is a line through EaEa parallel to APAP, db,dcd_b, d_c are defined in the same manner. Prove that three lines da,db,dcd_a, d_b, d_c are concurrent.
Nguyễn Tiến Lâm, Trần Quang Hùng
Euler Circleconcurrentgeometry