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ABTN is cyclic iff AB = AK, KT = KC,CN = BK (2017 Kyiv City MO Round2 11.2)

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September 10, 2020
geometrycyclic quadrilateralConcyclicequal segments

Problem Statement

The median CMCM is drawn in the triangle ABCABC intersecting bisector angle BLBL at point OO. Ray AOAO intersects side BCBC at point KK, beyond point KK draw the segment KT=KCKT = KC. On the ray BCBC beyond point CC draw a segment CN=BKCN = BK. Prove that is a quadrilateral ABTNABTN is cyclic if and only if AB=AKAB = AK.
(Vladislav Yurashev)
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