Question 46
Let $ABC$ be a right-angled triangle with the right angle at $C$, having sides of length $|AB| = 26$ and $|BC| = 24$. A semicircle with diameter on $\overline{BC}$ containing point $C$ is inscribed in the triangle. The semicircle touches the side $\overline{AB}$. What is the radius of the semicircle? (Nikola Adžaga)