Recall the following relation between the lengths of two secants:
[tex]|PA|\cdot|PB|=|PC|\cdot|PD|[/tex]
In the case of the given figure, we know that:
[tex]12\times(12+x)=14\times26[/tex]
Simplify the expressions and solve for x:
[tex]\begin{gathered} \Rightarrow12(12+x)=364 \\ \Rightarrow12\cdot12+12x=364 \\ \\ \Rightarrow144+12x=364 \\ \Rightarrow12x=364-144 \\ \Rightarrow12x=220 \\ \Rightarrow x=\frac{220}{12} \\ \Rightarrow x=18.33 \end{gathered}[/tex]
Therefore, the answer is:
[tex]x=18.33[/tex]
