MathNet 2019-part-01 — 184 problems (EN–VI) Question 170

The diagonals of a quadrilateral $ABCD$ intersect at the point $N$. It is known that the incircles of the triangles $ABN$ and $CBN$ are tangent to each other. Moreover, the incircles of the triangles $ADN$ and $CDN$ are tangent to each other as well.
Find all possible values of $AN : NC$.