Let B be the open unit ball in C 2 and let a, b, c be three points in C 2 which do not lie in a complex line, such that the complex line through a, b meets B and such that if one of the points a, b is in B and the other in C 2 \ B then a|b = 1 and such that at least one of the numbers a|c , b|c is different from 1. We prove that if a continuous function f on bB extends holomorphically into B along each complex line which meets {a, b, c}, then f extends holomorphically through B. This

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... the recent result of L. Baracco who proved such a result in the case when the points a, b, c are contained in B. The proof is quite different from the one of Baracco and uses the following one-variable result, which we also prove in the paper: Let Δ be the open unit disc in C. Given α ∈ Δ let C α be the family of all circles in Δ obtained as the images of circles centered at the origin under an automorphism of Δ that maps 0 to α. Given α, β ∈ Δ, α = β, and n ∈ N, a continuous function f on Δ extends meromorphically from every circle Γ ∈ C α ∪ C β through the disc bounded by Γ with the only pole at the center of Γ of degree not exceeding n if and only if f is of the form f (z) = a 0 (z)+a 1 (z)z+· · ·+a n (z)z n (z ∈ Δ) where the functions a j , 0 ≤ j ≤ n, are holomorphic on Δ.