4. Given point $P(-2,5)$ lies on the circle $C: x^{2}+y^{2}-2 x-2 y+F=0$, and the line $l: 3 x+4 y+8=0$ intersects the circle at points $A, B$, then $\overrightarrow{A B} \cdot \overrightarrow{B C}=$ $\qquad$
Solve
$4+25+4-10+F=0 \Rightarrow F=-23$, then the circle $C:(x-1)^{2}+(y-1)^{2}=25$. The distance from point $C$ to $AB$ is $d=\frac{3+4+8}{\sqrt{3^{2}+4^{2}}}=3 \Rightarrow|AB|=2 \sqrt{5^{2}-3^{2}}=8$, let the midpoint of $AB$ be $D$, then $\overrightarrow{AB} \cdot \overrightarrow{BC}=\overrightarrow{AB} \cdot(\overrightarrow{BD}+\overrightarrow{DC})=-\frac{1}{2}|AB|^{2}=-32$.