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IMOC 2017 G5 (<A=120 => E, F, Y,Z are concyclic, incenter related)

Source: https://artofproblemsolving.com/community/c6h1740077p11309077

March 20, 2020
Concyclicincentergeometry

Problem Statement

We have △ABC\vartriangle ABC with II as its incenter. Let DD be the intersection of AIAI and BCBC and define E,FE, F in a similar way. Furthermore, let Y=CI∩DE,Z=BI∩DFY = CI \cap DE, Z = BI \cap DF. Prove that if ∠BAC=120o\angle BAC = 120^o, then E,F,Y,ZE, F, Y,Z are concyclic. https://1.bp.blogspot.com/-5IFojUbPE3o/XnSKTlTISqI/AAAAAAAALd0/0OwKMl02KJgqPs-SDOlujdcWXM0cWJiegCK4BGAYYCw/s1600/imoc2017%2Bg5.png
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