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:**
Is line \( \overline{AB} \) a tangent to circle \( \bigodot C \)?
**Diagram Explanation:**
- There is a circle with center \( C \).
- Point \( A \) is on the circle.
- There are two lines: \( \overline{AC} \) with a length of 5, which is the radius of the circle, and \( \overline{AB} \), which is proposed to be a tangent.
- \( \overline{AB} \) extends from point \( A \), outside the circle, to point \( B \).
- The distances given are: \( \overline{AC} = 5 \), \( \overline{AB} = 14 \), and \( \overline{CB} = 15 \).
**Analysis:**
To determine if \( \overline{AB} \) is tangent, \( \overline{AC} \) and \( \overline{CB} \) must form a right triangle with \( \overline{AB} \) as the hypotenuse. Applying the Pythagorean theorem:
\[
5^2 + 14^2 = 25 + 196 = 221
\]
Since \( 221 \neq 15^2 \), which is 225, the segment \( \overline{AB} \) is not tangent to the circle at point \( A \).
**Your Answer:**
- No, \( \overline{AB} \) is not a tangent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88296449-4020-45ce-a35f-28e4157e48b0%2F7c59fce5-2fc9-46e4-9789-8a4a54140897%2Fwtrhiag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Is line \( \overline{AB} \) a tangent to circle \( \bigodot C \)?
**Diagram Explanation:**
- There is a circle with center \( C \).
- Point \( A \) is on the circle.
- There are two lines: \( \overline{AC} \) with a length of 5, which is the radius of the circle, and \( \overline{AB} \), which is proposed to be a tangent.
- \( \overline{AB} \) extends from point \( A \), outside the circle, to point \( B \).
- The distances given are: \( \overline{AC} = 5 \), \( \overline{AB} = 14 \), and \( \overline{CB} = 15 \).
**Analysis:**
To determine if \( \overline{AB} \) is tangent, \( \overline{AC} \) and \( \overline{CB} \) must form a right triangle with \( \overline{AB} \) as the hypotenuse. Applying the Pythagorean theorem:
\[
5^2 + 14^2 = 25 + 196 = 221
\]
Since \( 221 \neq 15^2 \), which is 225, the segment \( \overline{AB} \) is not tangent to the circle at point \( A \).
**Your Answer:**
- No, \( \overline{AB} \) is not a tangent.
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