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11 votes
in the figure below, two seconds are drawn to a circle from an exterior point E. Suppose that EZ = 16.8, EX = 14, and EW =35. Find XY.

in the figure below, two seconds are drawn to a circle from an exterior point E. Suppose-example-1
User Leaniman
by
3.0k points

1 Answer

9 votes
9 votes

Knowing that two secants are drawn to a circle from an exterior point, you need to use the Intersecting Secant Theorem.

Based on the Intersecting Secant Theorem, you can write the following equation:


EZ\cdot EW=EX\cdot EY

Knowing that:


\begin{gathered} EZ=16.8 \\ EX=14 \\ EW=35 \end{gathered}

Substitute those values into the equation:


(16.8)(35)=(14)\cdot EY

Solve for EY:


\begin{gathered} 588=14EY \\ EY=(588)/(14) \\ EY=42 \end{gathered}

Notice that:


EY=EX+XY

Then you can substitute values and solve for XY:


\begin{gathered} 42=14+XY \\ 42-14=XY \\ XY=28 \end{gathered}

The answer is:


XY=28

User Elias Vargas
by
2.7k points
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