= Solution
Each <calcium> <cation> has eight <fluoride> neighbours at the vertices of a <cube>: <cubic coordination>. Each <fluoride> <anion> has four <calcium> neighbours in <tetrahedral coordination>. Both unlike-neighbour <Euclidean distances> are $\sqrt3a/4$, with $a$ the conventional cubic <lattice parameter>.
Apply the <Goldschmidt packing principle> at its limiting eight-coordinate geometry: the eight surrounding <anions> just touch one another and also touch the central <cation>. The <anions> form a <cube> of edge $a/2$, so $2r_a=a/2$ and $r_a+r_c=\sqrt3a/4$. Eliminating $a$ gives
$$
\boxed{\frac{r_a}{r_c}=\frac1{\sqrt3-1}=\frac{\sqrt3+1}{2}\simeq1.366.}
$$
Equivalently, $r_c/r_a=0.732$. This is a limiting <radius ratio rule>, rather than a measured ionic-radius ratio. It does not assume that the <calcium> sublattice consists of mutually touching <spheres>: the <calcium> positions have face-centred cubic symmetry, but that symmetry alone does not specify which <ions> touch. A different construction with touching <calcium> <spheres> and <fluoride> just filling their <tetrahedral interstitial sites> would instead give $r_a/r_c=\sqrt{3/2}-1=0.225$; that is the opposite contact limit, not the eight-coordinate anion-contact ideal used here.
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