10. In the figure, AC is tangent to circle D at point C. D & B A Part A If mA = 38°, what is the measure of BC in degrees? Part B If AC = 5 m and DC = 4 m, what is the length of AD in meters?
10. In the figure, AC is tangent to circle D at point C. D & B A Part A If mA = 38°, what is the measure of BC in degrees? Part B If AC = 5 m and DC = 4 m, what is the length of AD in meters?
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
100%
Answer question 10
Here is the diagram's details:
- A circle with center \( D \).
- Radius \( DC \) perpendicular to the tangent \( AC \) at point \( C \).
- Point \( A \) is outside the circle.
- \( B \) is a point on \( AC \), inside the circle, creating segment \( BC \).
**Part A**
If \( m \angle A = 38^\circ \), what is the measure of \( \overarc{BC} \) in degrees?
**Part B**
If \( AC = 5 \, \text{m} \) and \( DC = 4 \, \text{m} \), what is the length of \( AD \) in meters?
#### Diagram Explanation
In the provided figure, point \( A \) lies outside of circle \( D \). Line segment \( AC \) is tangent to the circle at point \( C \). A line segment \( DC \) is drawn from the center \( D \) of the circle to the tangent point \( C \), which is perpendicular to the tangent line \( AC \). Point \( B \) lies on the line segment \( AC \) within the circle, creating a chord \( BC \).
- **Part A** involves finding the measure of the angle subtended by the arc \( BC \).
- **Part B** requires calculating the length of the segment \( AD \) using given measurements of \( AC \) and \( DC \).
#### Calculation Notes for Part B
You will use the Pythagorean theorem to find \( AD \). Given \( AC \) (tangent) and \( DC \) (radius perpendicular to the tangent at the point of tangency), the distance \( AD \) (hypotenuse of right triangle \( ADC \)) can be calculated as:
\[ AD = \sqrt{AC^2 + DC^2} \]
By plugging the values:
\[ AC = 5 \, \text{m}, \, DC = 4 \, \text{m} \]
Thus,
\[ AD = \sqrt{(5)^2 + (4)^2} = \sqrt{25 + 16} = \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff84e6597-46e6-44a4-8897-2a199b4e6fb0%2F6b09de86-fa48-4f26-951b-2abcba815a64%2Ft9gud2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem
#### Problem Statement
In the figure, \( AC \) is tangent to circle \( D \) at point \( C \).
Here is the diagram's details:
- A circle with center \( D \).
- Radius \( DC \) perpendicular to the tangent \( AC \) at point \( C \).
- Point \( A \) is outside the circle.
- \( B \) is a point on \( AC \), inside the circle, creating segment \( BC \).
**Part A**
If \( m \angle A = 38^\circ \), what is the measure of \( \overarc{BC} \) in degrees?
**Part B**
If \( AC = 5 \, \text{m} \) and \( DC = 4 \, \text{m} \), what is the length of \( AD \) in meters?
#### Diagram Explanation
In the provided figure, point \( A \) lies outside of circle \( D \). Line segment \( AC \) is tangent to the circle at point \( C \). A line segment \( DC \) is drawn from the center \( D \) of the circle to the tangent point \( C \), which is perpendicular to the tangent line \( AC \). Point \( B \) lies on the line segment \( AC \) within the circle, creating a chord \( BC \).
- **Part A** involves finding the measure of the angle subtended by the arc \( BC \).
- **Part B** requires calculating the length of the segment \( AD \) using given measurements of \( AC \) and \( DC \).
#### Calculation Notes for Part B
You will use the Pythagorean theorem to find \( AD \). Given \( AC \) (tangent) and \( DC \) (radius perpendicular to the tangent at the point of tangency), the distance \( AD \) (hypotenuse of right triangle \( ADC \)) can be calculated as:
\[ AD = \sqrt{AC^2 + DC^2} \]
By plugging the values:
\[ AC = 5 \, \text{m}, \, DC = 4 \, \text{m} \]
Thus,
\[ AD = \sqrt{(5)^2 + (4)^2} = \sqrt{25 + 16} = \
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 4 steps with 5 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning