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Nice geometry

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January 9, 2017
geometrycircumcircle

Problem Statement

LL is a Line that intersect with the side AB,BC,ACAB,BC,AC of triangle ABCABC at F,D,EF,D,E The line perpendicular to BCBC from DD intersect AB,ACAB,AC at A1,A2A_{1},A_{2} respectively Name B1,B2,C1,C2B_{1},B_{2},C_{1},C_{2} similarly Prove that the circumcenters of AA1A2,BB1B2,CC1C2AA_{1}A_{2},BB_{1}B_{2},CC_{1}C_{2} are collinear
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