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Geometry Mathley 4.4 4 euler lines concurrent

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June 7, 2020
geometryEuler LineconcurrentEuler Circle

Problem Statement

Let ABCABC be a triangle with EE being the centre of its Euler circle. Through EE, construct the lines PS,MQ,NRPS, MQ, NR parallel to BC,CA,ABBC,CA,AB (R,QR,Q are on the line BC,N,PBC, N, P on the line AC,M,SAC,M, S on the line ABAB). Prove that the four Euler lines of triangles ABC,AMN,BSR,CPQABC,AMN,BSR,CPQ are concurrent.
Nguyễn Văn Linh
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