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Geometry Mathley 14.4 concurrency related to NPC centers

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June 7, 2020
Euler Circleconcurrentgeometry

Problem Statement

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
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