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KöMaL Geometry

Source: KöMaL A. 805

March 23, 2022
geometrykomalEuler Line

Problem Statement

In acute triangle ABC,ABC, the feet of the altitudes are A1,B1,A_1,B_1, and C1C_1 (with the usual notations on sides BC,CA,BC,CA, and ABAB respectively). The circumcircles of triangles AB1C1AB_1C_1 and BC1A1BC_1A_1 intersect at the circumcircle of triangle ABCABC ar points P≠AP\neq A and Q≠B,Q\neq B, respectively. Prove that lines AQ,BPAQ, BP and the Euler line of triangle ABCABC are either concurrent or parallel to each other.
Proposed by Géza Kós, Budapest
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