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Why no normal geometry :(

Source: Bolivia Ibero TST 2021 Day 2 P2

September 2, 2022
geometryBoliviaTSTisosceles

Problem Statement

On a isosceles triangle △ABC\triangle ABC with AB=BCAB=BC let K,MK,M be the midpoints of AB,ACAB,AC respectivily. Let (CKB)(CKB) intersect BMBM at N≠MN \ne M, the line through NN parallel to ACAC intersects (ABC)(ABC) at A1,C1A_1,C_1. Show that △A1BC1\triangle A_1BC_1 is equilateral.
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