On sets without tangents in Galois planes of even order

A study on sets without tangents in Galois planes of even order is presented. Examples are given for small sets without tangents but having odd lines. It is shown that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2,q), q even, is at least q+1+√q/6 provided that the set is not of even type