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We investigate differential geometric properties of a parabolic point of asurface in the Euclidean three space. We introduce the contact cylindricalsurface which is a cylindrical surface having a degenerate contact type withthe original surface at a parabolic point. Furthermore, we show that such acontact property gives a characterization to the $\mathcal{A}$-singularity ofthe orthogonal projection of a surface from the asymptotic direction.

Contact cylindrical surfaces and a projection of a surface around a parabolic point