SOLUTION
The diagram shows an image of intersecting secants. We would use the intersecting secants theorem in the image below to solve the question.
We compare the image above with the diagram in the question
This implies that the solution would be
[tex]\begin{gathered} AE\times AD=AB\times AC \\ \end{gathered}[/tex]AE=21+9=30
AD=9
AB=10
AC=10+x
Substituting the parameters in the secant theorem above, we then have;
[tex]\begin{gathered} 30\times9=10\times(10+x) \\ 270=100+10x \\ 10x=270-100 \\ 10x=170 \\ x=\frac{170}{10} \\ x=17 \\ \end{gathered}[/tex]Therefore, the length of x is 17
