MathNet 2015-part-07 — 185 problems (EN–VI) Question 79

$ABCD$ is a cyclic quadrilateral with sides $AB = 10$, $BC = 8$, $CD = 25$, and $DA = 12$. A circle $\omega$ is tangent to segments $DA$, $AB$, and $BC$. Find the radius of $\omega$.