[tex]A)6[/tex]
1) In this diagram we can see two secant lines crossing that circle. Therefore we can write out the following relation, calling P the point where the secant lines come.
[tex]\begin{gathered} PA\cdot PB=PC\cdot PD \\ 4\mleft(4+x\mright)=5\mleft(5+3\mright) \\ 16+4x=25+15 \\ 16+4x=40 \\ 4x=40-16 \\ 4x=24 \\ \frac{4x}{4}=\frac{24}{4} \\ x=6 \end{gathered}[/tex]
Thus, the answer is A) x=6
