Perpendicular bisectors and orthogonality

In a real normed space $ (E, \| \cdot \|) $ we consider the perpendicular bisectors associated to any linear segment, and using them we give some characterizations of inner product spaces. Based on the properties of the perpendicular bisectors in the real plane, we introduce a new orthogonal relation in $ (E, \| \cdot \|) $ and its properties are investigated.