8. Through a point $P$ on a sphere with radius 5, three mutually perpendicular chords $P A, P B$, and $P C$ are drawn such that $P A=2 P B$. Then the maximum value of $P A+P B+P C$ is $\qquad$ .
Let $P A=2 x, P B=x, P C=y$, then $P A^{2}+P B^{2}+P C^{2}=5 x^{2}+y^{2}=100$, so $(P A+P B+P C)^{2}=(3 x+y)^{2} \leqslant\left[\left(\frac{3}{\sqrt{5}}\right)^{2}+1\right]\left(5 x^{2}+y^{2}\right)=280$ $\Rightarrow P A+P B+P C \leqslant 2 \sqrt{70}$, equality holds when $\frac{5 x}{3}=y \Rightarrow x=\frac{30}{\sqrt{70}}, y=\frac{50}{\sqrt{70}}$.