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Reflection of circumcenter

Source: KJMO 2018 p5

July 26, 2019
geometrygeometric transformationreflectioncircumcircle

Problem Statement

Let there be an acute scalene triangle ABCABC with circumcenter OO. Denote D,ED,E be the reflection of OO with respect to AB,ACAB,AC, respectively. The circumcircle of ADEADE meets ABAB, ACAC, the circumcircle of ABCABC at points K,L,MK,L,M, respectively, and they are all distinct from AA. Prove that the lines BC,KL,AMBC,KL,AM are concurrent.
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