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I am attaching a picture of the question as you can see the answer has already been picked well my teacher wants me to show how she got that answer.

I am attaching a picture of the question as you can see the answer has already been picked well my teacher wants me to show how she got that answer class=

Respuesta :

From the properties of the circle we know that:

[tex]\begin{gathered} 6(2x-2+6)=5(31+5) \\ 6(2x+4)=5(36) \\ 12x+24=180 \\ 12x=180-24 \\ 12x=156 \\ x=\frac{156}{12} \\ x=13 \end{gathered}[/tex]

This comes from the fact that If two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal. In this case this means that:

[tex]DE\cdot DF=DC\cdot DB[/tex]

Now that we know the value of x we plug it in the expression for EF:

[tex]2(13)-2=26-2=24[/tex]

Therefore segment EF is equal to 24.

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