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
Related questions
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.
\[
\begin{array}{c}
\quad \quad \quad \quad x \quad \quad
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87c6590a-3759-4f4e-bb57-64d6c25bd8a3%2F18637c30-7cad-4d00-a66c-4e84a7352c6e%2F0e6ipx4_processed.jpeg&w=3840&q=75)
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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