ANSWER
c = 6.4
EXPLANATION
The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:
[tex]9\cdot(9+19)=13\cdot(13+c)[/tex]
Solving for c:
[tex]\begin{gathered} 9\cdot28=13^2+13c \\ 252=169+13c \\ 252-169=13c \\ 83=13c \\ c=\frac{83}{13} \\ c=6.3846\ldots \\ c\approx6.4 \end{gathered}[/tex]
