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two segments from P are tangent to circle O. If the measure of and P is 60 and the radius of circle O is 12 feet, find the length of each tangent.

two segments from P are tangent to circle O If the measure of and P is 60 and the radius of circle O is 12 feet find the length of each tangent class=

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SOLUTION

Consider the sketch sown below

Using tangent ratio it follows

[tex]\tan30=\frac{12}{x}[/tex]

This gives

[tex]\begin{gathered} x=\frac{12}{\tan30} \\ x=\frac{12}{\frac{1}{\sqrt{3}}} \\ x=12\sqrt{3} \end{gathered}[/tex]

Therefore the lengths of each tangent is 12 times square root of 3

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