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Concyclic points

Source: Greek IMO TST,2013,Pr.2

August 16, 2014
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCABC be a non-isosceles,aqute triangle with AB<ACAB<AC inscribed in circle c(O,R)c(O,R).The circle c1(B,AB)c_{1}(B,AB) crosses ACAC at KK and cc at EE. KEKE crosses cc at FF and BOBO crosses KEKE at LL and ACAC at MM while AEAE crosses BFBF at DD.Prove that: i)D,L,M,FD,L,M,F are concyclic. ii)B,D,K,M,EB,D,K,M,E are concyclic.
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