Δευτέρα, 1 Ιανουαρίου 2018

2005 JBMO Shortlist 9

Let $C_1,C_2$ be two circles intersecting at points $A,P$  with centers $O,K$ respectively. Let $B,C$ be the symmetric of $A$ wrt $O,K$ in circles $C_1,C_2 $ respectively. A random line passing through $A$ intersects circles $C_1,C_2$ at $D,E$ respectively.  Prove that the center of circumcircle of triangle $DEP$  lies on the  circumcircle of triangle $OKP$.


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