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 21:**
In the circle below, \( AC \) and \( BC \) are tangents.
**Diagram Explanation:**
- A circle with center at an unspecified point.
- Point \( A \) and point \( B \) are on the circle.
- Tangents \( AC \) and \( BC \) meet at point \( C \) outside the circle.
- Line segment \( AC \) is labeled \( 17 \).
- Line segment \( BC \) is labeled \( 3y - 4 \).
- Point \( D \) lies on the circle, on the same side as point \( A \).
**Question:**
Solve for the value of \( y \).
**Answer Box:**
\( y = \) \[\_\_\_\_\_\_\_\_\]
**Additional Note:**
Since \( AC \) and \( BC \) are tangents from a common external point \( C \) to the circle, they are equal in length. Therefore, the equation can be set up as:
\[ AC = BC \]
\[ 17 = 3y - 4 \]
This information allows for solving \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43d2448d-3e96-4e40-abdb-281cc47928a3%2Feee65497-ce32-419b-beb2-9349fa80da07%2Fksse4lb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 21:**
In the circle below, \( AC \) and \( BC \) are tangents.
**Diagram Explanation:**
- A circle with center at an unspecified point.
- Point \( A \) and point \( B \) are on the circle.
- Tangents \( AC \) and \( BC \) meet at point \( C \) outside the circle.
- Line segment \( AC \) is labeled \( 17 \).
- Line segment \( BC \) is labeled \( 3y - 4 \).
- Point \( D \) lies on the circle, on the same side as point \( A \).
**Question:**
Solve for the value of \( y \).
**Answer Box:**
\( y = \) \[\_\_\_\_\_\_\_\_\]
**Additional Note:**
Since \( AC \) and \( BC \) are tangents from a common external point \( C \) to the circle, they are equal in length. Therefore, the equation can be set up as:
\[ AC = BC \]
\[ 17 = 3y - 4 \]
This information allows for solving \( y \).
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