Let be a Hermitian curve and let Γ be a conic of PG(2, q 2). In this paper we determine the possible intersection configurations between Γ and under the hypotheses that Γ and either share two points with the same tangent lines or contain a common Baer subconic. Moreover, the intersection configurations between a degenerate Hermitian curve and a conic sharing a Baer subconic are also determined.
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