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Mathley 2014.2 p3 by Tran Quang Hung

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August 20, 2020
geometryconcurrentreflection

Problem Statement

In a triangle ABCABC, DD is the reflection of AA about the sideline BCBC. A circle (K)(K) with diameter ADAD meets DB,DCDB,DC at M,NM,N which are distinct from DD. Let E,FE,F be the midpoint of CA,ABCA,AB. The circumcircles of KEM,KFNKEM,KFN meet each other again at LL, distinct from KK. Let KLKL meets EFEF at XX; points Y,ZY,Z are defined in the same manner. Prove that three lines AX,BY,CZAX,BY,CZ are concurrent.
Tran Quang Hung, Dean of the Faculty of Science, Thanh Xuan, Hanoi.
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