Question

With the two secants intersecting outside the circle, what is the length of the section labeled X?

Answer 1

Recall the following relation between the lengths of two secants:

`|PA|\cdot|PB|=|PC|\cdot|PD|`

In the case of the given figure, we know that:

`12*(12+x)=14*26`

Simplify the expressions and solve for x:

`\begin{gathered} \Rightarrow12(12+x)=364 \\ \Rightarrow12\cdot12+12x=364 \\ \\ \Rightarrow144+12x=364 \\ \Rightarrow12x=364-144 \\ \Rightarrow12x=220 \\ \Rightarrow x=(220)/(12) \\ \Rightarrow x=18.33 \end{gathered}`

Therefore, the answer is:

`x=18.33`