Find the value of x in the figure below. Assume lines that look like tangents are tangents. 3x+18 Xx=2 B. x=4.67 23) 60x-24 C. x=20.67 D. x = 14
Find the value of x in the figure below. Assume lines that look like tangents are tangents. 3x+18 Xx=2 B. x=4.67 23) 60x-24 C. x=20.67 D. x = 14
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 46E
Related questions
Question
Help #23
![**Mathematics Problem: Circle and Tangent Analysis**
**Problem Statement:**
Find the value of \( x \) in the figure below. Assume lines that look like tangents are tangents.
**Figure Explanation:**
The figure provided displays a circle with center \( O \) and two tangent lines originating from the point \( P \) outside the circle. The tangents touch the circle at points \( A \) and \( B \), respectively. There are two expressions associated with the segments from \( P \) to the tangency points:
- \( PA = 3x + 18 \)
- \( PB = 6x - 24 \)
**Options:**
A. \( x = 2 \) (crossed out)
B. \( x = 4.67 \)
C. \( x = 20.67 \)
D. \( x = 14 \)
**Solution Explanation:**
Given that \( PA \) and \( PB \) are tangents drawn from a common external point to a circle, they are equal in length:
\[ PA = PB \]
\[ 3x + 18 = 6x - 24 \]
Solving for \( x \):
1. Rearrange the equation:
\[ 18 + 24 = 6x - 3x \]
2. Simplify:
\[ 42 = 3x \]
3. Divide both sides by 3:
\[ x = 14 \]
**Correct Answer:**
D. \( x = 14 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4904ad93-6dcc-43fa-9122-8f69394907f2%2F7c1fefc2-d2a7-485c-832b-4a7aa7cf8e3b%2Fgeob9z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem: Circle and Tangent Analysis**
**Problem Statement:**
Find the value of \( x \) in the figure below. Assume lines that look like tangents are tangents.
**Figure Explanation:**
The figure provided displays a circle with center \( O \) and two tangent lines originating from the point \( P \) outside the circle. The tangents touch the circle at points \( A \) and \( B \), respectively. There are two expressions associated with the segments from \( P \) to the tangency points:
- \( PA = 3x + 18 \)
- \( PB = 6x - 24 \)
**Options:**
A. \( x = 2 \) (crossed out)
B. \( x = 4.67 \)
C. \( x = 20.67 \)
D. \( x = 14 \)
**Solution Explanation:**
Given that \( PA \) and \( PB \) are tangents drawn from a common external point to a circle, they are equal in length:
\[ PA = PB \]
\[ 3x + 18 = 6x - 24 \]
Solving for \( x \):
1. Rearrange the equation:
\[ 18 + 24 = 6x - 3x \]
2. Simplify:
\[ 42 = 3x \]
3. Divide both sides by 3:
\[ x = 14 \]
**Correct Answer:**
D. \( x = 14 \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning