Let P be a point in the plane of \Delta ABC with points A', B', C' on the cevians AP, BP, CP, respectively. Assume that the circumcircles (Oa), (Ob), (Oc), of the triples \{P, B', C'\}, \{P, C', A'\}, \{P, A', B'\}, intersect sides BC, AC, AB in \{A1, A2\}, \{B1, B2\}, \{C1, C2\}, respectively. Then the six points A1, A2, B1, B2, C1, C2 are concyclic.

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