MathNet 2018-part-07 — 177 problems (EN–VI) Question 132

Triangle $\triangle P Q R$, with $P Q = P R = 5$ and $Q R = 6$, is inscribed in circle $\omega$. Compute the radius of the circle with center on $\overline{Q R}$ which is tangent to both $\omega$ and $\overline{P Q}$.