Question

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.

Answer 1

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:

$\begin{gathered} 588=14EY \\ EY=\frac{588}{14} \\ EY=42 \end{gathered}$

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:

$XY=28$