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Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
Question 5 please
Below are three different geometric problems involving circles and chords or secants. Each problem requires solving for the variable \(x\).

**Problem 3:**

There is a circle with a secant and a chord intersecting inside it. The lengths indicated are 4, 5, and 10, while \(x\) is the unknown segment.

\[
\begin{array}{c}
   \ \quad\quad \ 4 \quad \quad \ \ \ \\    
(\begin{array}{c}

      \quad\quad\quad\quad\quad \ \   5 \quad \quad \
\end{array})\\
(\begin{array}{c}
    \quad\quad\ secant\ ) = 10 
\end{array})\\(\begin{array}{c}

   ( \begin{array}{c}
       chord = x
\end{array})
)
\end{array})(

\begin{array}{c}
)\

\end{array})\\)
 \end{array})

\]
(Note: Figure indicates labeling)

**Problem 5:**

There is a circle with a triangle formed outside the circle, creating two segments with lengths 4 and 5 respectively. Another segment of length 3 is intersected, with the variable \(x\) as an additional segment in the triangle.

\[
\begin{array}{c}
\quad\quad\quad 4\quad\quad \\
 \begin{array}{c}
     /\\
    / \\
   / \\
  /
 \end{array} 
\quad /
 \end{array}\\
\begin{array}{c}
\quad \quad \ \quad 5 \\ 
(\begin{array}{c}
  \quad \quad \quad\ \  3\quad \quad
 \end{array})(
 \begin{array}{c}
   chord = x 
\end{array})
\end{array})
\]

(Note: Figure indicates labeling)

**Problem 7:**

There is another circle with a secant segment that produces a chord inside the circle. The segments inside the circle are labeled 8 and 7, while a larger outer segment is labeled 14. The variable \(x\) is part of the secant configuration.

\[
\begin{array}{c}
 \quad \quad  \quad \quad  x \quad \quad 
\
Transcribed Image Text:Below are three different geometric problems involving circles and chords or secants. Each problem requires solving for the variable \(x\). **Problem 3:** There is a circle with a secant and a chord intersecting inside it. The lengths indicated are 4, 5, and 10, while \(x\) is the unknown segment. \[ \begin{array}{c} \ \quad\quad \ 4 \quad \quad \ \ \ \\ (\begin{array}{c} \quad\quad\quad\quad\quad \ \ 5 \quad \quad \ \end{array})\\ (\begin{array}{c} \quad\quad\ secant\ ) = 10 \end{array})\\(\begin{array}{c} ( \begin{array}{c} chord = x \end{array}) ) \end{array})( \begin{array}{c} )\ \end{array})\\) \end{array}) \] (Note: Figure indicates labeling) **Problem 5:** There is a circle with a triangle formed outside the circle, creating two segments with lengths 4 and 5 respectively. Another segment of length 3 is intersected, with the variable \(x\) as an additional segment in the triangle. \[ \begin{array}{c} \quad\quad\quad 4\quad\quad \\ \begin{array}{c} /\\ / \\ / \\ / \end{array} \quad / \end{array}\\ \begin{array}{c} \quad \quad \ \quad 5 \\ (\begin{array}{c} \quad \quad \quad\ \ 3\quad \quad \end{array})( \begin{array}{c} chord = x \end{array}) \end{array}) \] (Note: Figure indicates labeling) **Problem 7:** There is another circle with a secant segment that produces a chord inside the circle. The segments inside the circle are labeled 8 and 7, while a larger outer segment is labeled 14. The variable \(x\) is part of the secant configuration. \[ \begin{array}{c} \quad \quad \quad \quad x \quad \quad \
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