  We study non-geodesic Funk-type transforms associated with cross-sections of
the n-sphere by k-dimensional planes passing through an arbitrary fixed point
inside the sphere. The main results include injectivity conditions for these
transforms, inversion formulas, and connection with geodesic Funk transforms.
We also show that, unlike the case of planes through a single common center,
the integrals over spherical sections by planes through two distinct centers
provide the corresponding reconstruction problem a unique solution.
