question
given the circle below with secant $ \overline { g f e } $ and tangent $ \overline { d e } $, find the length of $ \overline { d e } $.
round to the nearest tenth if necessary.
answer

Question

Accepted Answer

# Explanation:
## Step1: Use the tangent - secant theorem
The tangent - secant theorem states that if a tangent segment $DE$ and a secant segment $GFE$ are drawn to a circle from an external point $E$, then $DE^{2}=EF\times EG$.
We know that $EF = 27$ and $EG=EF + FG=27 + 14=41$.
## Step2: Calculate $DE$
Substitute the values into the formula $DE^{2}=EF\times EG$. So $DE^{2}=27\times41$.
$$
\begin{align*}
DE^{2}&=27\times41\
DE^{2}&=1107\
DE&=\sqrt{1107}\
DE&\approx33.3
\end{align*}
$$

# Answer:
$DE\approx33.3$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the tangent - secant theorem

Step2: Calculate \(DE\)

Answer: