  We calculate the Chern-Simons invariants of the twist knot orbifolds using
the Schl\"{a}fli formula for the generalized Chern-Simons function on the
family of the twist knot cone-manifold structures. Following the general
instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present the
concrete formulae and calculations. We use the Pythagorean Theorem \cite{HMP}
to relate the complex length of the longitude and the complex distance between
the two axes fixed by two generators. As an application, we calculate the
Chern-Simons invariants of cyclic coverings of the hyperbolic twist knot
orbifolds.
  We also derive some interesting results. The $A$-polynomials of twist knots
are obtained from the complex distance polynomials. Hence the edge polynomials
corresponding to the edges of the Newton polygons of A-polynomials of twist
knots can be obtained. In particular, the number of boundary components of
every incompressible surface corresponding to slope $-4n+2$ appear to be $2$.
