6. The base of the triangular pyramid $S A B C$ is an equilateral triangle $A B C$ with a side length of 8. The lateral edge $S C$ is perpendicular to the base and has a length of 15. A sphere with center $O$ lying in the plane $S B C$ touches the edges $S A$, $A B$, and $A C$ at points $A_{1}$, $B_{1}$, and $C_{1}$, respectively. Find $A A_{1}$, the distance from point $O$ to the edge $B C$, and the radius of the sphere.
Answer: $A A_{1}=6, \quad$ distance $=\frac{18}{5}, \quad$ radius $=\frac{4 \sqrt{39}}{5}$.