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hard question 1

Source: iran tst 2014 third exam

May 22, 2014
circumcirclegeometry proposed

Problem Statement

The incircle of a non-isosceles triangle ABCABC with the center II touches the sides BC,AC,ABBC,AC,AB at A1,B1,C1A_{1},B_{1},C_{1} . let AI,BI,CIAI,BI,CI meets BC,AC,ABBC,AC,AB at A2,B2,C2A_{2},B_{2},C_{2}. let A′A' is a point on AIAI such that A1A′⊥B2C2A_{1}A'\perp B_{2}C_{2} .B′,C′B',C' respectively. prove that two triangle A′B′C′,A1B1C1A'B'C',A_{1}B_{1}C_{1} are equal.
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