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Meh geo, as always

Source: Iranian TST 2021, first exam day 2, problem 6

May 17, 2021
geometryEuler Line

Problem Statement

Point DD is chosen on the Euler line of triangle ABCABC and it is inside of the triangle. Points E,FE,F are were the line BD,CDBD,CD intersect with AC,ABAC,AB respectively. Point XX is on the line ADAD such that ∠EXF=180−∠A\angle EXF =180 - \angle A, also A,XA,X are on the same side of EFEF. If PP is the second intersection of circumcircles of CXF,BXECXF,BXE then prove the lines XP,EFXP,EF meet on the altitude of AA
Proposed by Alireza Danaie
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