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TOT 2000 Autumn OS1 isosceles wanted, circles related

Source:

May 11, 2020
geometryisoscelescircles

Problem Statement

Triangle ABCABC is inscribed in a circle. Chords AMAM and ANAN intersect side BCBC at points KK and LL respectively. Prove that if a circle passes through all of the points K,L,MK, L, M and NN, then ABCABC is an isosceles triangle.
(V Zhgun)
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