2018 JBMO Problems

Problem 4

Let $\triangle ABC$ and $A'$ , $B'$ , $C'$ the symmetrics of vertex over opposite sides.The intersection of the circumcircles of $\triangle ABB'$ and $\triangle ACC'$ is $A_1$ . $B_1$ and $C_1$ are defined similarly.Prove that lines $AA_1$ , $BB_1$ and $CC_1$ are concurent.

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2018 JBMO Problems

Problem 4