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

With The Two Secants Intersecting Outside The Circle What Is The Length Of The Section Labeled X class=

Sagot :

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]

View image BaxterR14144
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