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Three collinear points

Source: Serbian JBMO TST 2018, problem 1

May 21, 2018
geometry

Problem Statement

Let ADAD be an internal angle bisector in triangle ΔABC\Delta ABC. An arbitrary point MM is chosen on the closed segment ADAD. A parallel to BCBC through MM cuts ABAB at NN. Let AD,CMAD, CM cut circumcircle of ΔABC\Delta ABC at K,LK, L, respectively. Prove that K,N,LK,N,L are collinear.
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