MathNet 2017-part-01 — 176 problems (EN–VI) Question 151

Let $S$ and $T$ be points inside the triangle $ABC$. The distance from $S$ to lines $AB$, $BC$ and $CA$ is $10$, $7$ and $4$, respectively. The distance from $T$ to these lines is $4$, $10$ and $16$, respectively.
Determine the radius of the incircle of triangle $ABC$.