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Where is the center? on M I_a

Source: Iranian Third Round 2020 Geometry exam Problem3

November 18, 2020
geometryexcircle

Problem Statement

The circle Ω\Omega with center IAI_A, is the AA-excircle of triangle ABCABC. Which is tangent to AB,ACAB,AC at F,EF,E respectivly. Point DD is the reflection of AA through IABI_AB. Lines DIADI_A and EFEF meet at KK. Prove that ,circumcenter of DKEDKE , midpoint of BCBC and IAI_A are collinear.
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