Παρασκευή, 13 Οκτωβρίου 2017

2004 JBMO Shortlist 10

Let  $ABC$ be a triangle with $m (\angle C) = 90^\circ$  and the points $D \in [AC], E\in [BC]$. Inside the triangle we construct the semicircles $C_1, C_2, C_3, C_4$ of diameters $[AC], [BC], [CD], [CE]$ and let  $\{C, K\} = C_1 \cap C_2, \{C, L\} = C_2 \cap C_3, \{C, N\} =C_1 \cap C_4$. Show that points $K, L, M, N$ are concyclic.

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