I don't know if there is a name of such a thing, but I would be thankful for each help.
I have an ellispoid (exactly it's an oblate ellipsoid) with with equatorial radius $a$ and a polar radius $b$.
At a given (geodetic) Latitude $φ$ is there a point $P$ at the surface of this ellipsoid , I would to draw a sphere inside the ellipsoid fitting and it's tangent at $P$ .
Which radius $R$ should it have? And where should the coordinates of its center $A (x, y, z)$ be?
Thanks in advance