182 CHAPTER 3 Foundations of Geometry 2 (b) Drag Cto such a position that ray BC lies exterior to LBAB', What happens to the locus of D in this case? Is your knowledge of Euclidean geometry sufficient for you to explain this behavior? 3.7 Quad (a) (b) MLCBA = 32.64° %3D mZCBA = 11.95° A B D. 10. Assume the usual definition for circles. Consider the concentric circles in the figure, and show that if OA and OB are radii of the smaller of the two circles, and LOAC =LOBD, then AC = BD. 11. Prove that if I is any point on the bisector BD of LABC, then I is an interior point of the angle and is equidistant from its sides, and conversely. *12. Prove that the angle bisectors of any triangle are concurrent at a point I, called the incenter, that is equidistant from the three sides of the triangle. (Hint: Use the re- sult of Problem 11; the argument is virtually the same as that for the concurrence of the perpendicular bisectors of the sides of a triangle, Problem 20, Section 3.3.) D *This result is needed for Problem 14, Section 3.8.
182 CHAPTER 3 Foundations of Geometry 2 (b) Drag Cto such a position that ray BC lies exterior to LBAB', What happens to the locus of D in this case? Is your knowledge of Euclidean geometry sufficient for you to explain this behavior? 3.7 Quad (a) (b) MLCBA = 32.64° %3D mZCBA = 11.95° A B D. 10. Assume the usual definition for circles. Consider the concentric circles in the figure, and show that if OA and OB are radii of the smaller of the two circles, and LOAC =LOBD, then AC = BD. 11. Prove that if I is any point on the bisector BD of LABC, then I is an interior point of the angle and is equidistant from its sides, and conversely. *12. Prove that the angle bisectors of any triangle are concurrent at a point I, called the incenter, that is equidistant from the three sides of the triangle. (Hint: Use the re- sult of Problem 11; the argument is virtually the same as that for the concurrence of the perpendicular bisectors of the sides of a triangle, Problem 20, Section 3.3.) D *This result is needed for Problem 14, Section 3.8.
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
Topic Video
Question
Please answer question 10
![182
CHAPTER 3 Foundations of Geometry 2
(b) Drag Cto such a position that ray BC lies exterior to LBAB', What happens to
the locus of D in this case? Is your knowledge of Euclidean geometry sufficient
for you to explain this behavior?
3.7 Quad
(a)
(b)
MLCBA = 32.64°
%3D
mZCBA = 11.95°
A
B
D.
10. Assume the usual definition for circles. Consider the concentric circles in the figure,
and show that if OA and OB are radii of the smaller of the two circles, and
LOAC =LOBD, then AC = BD.
11. Prove that if I is any point on the bisector BD of LABC, then I is an interior point
of the angle and is equidistant from its sides, and conversely.
*12. Prove that the angle bisectors of any triangle are concurrent at a point I, called the
incenter, that is equidistant from the three sides of the triangle. (Hint: Use the re-
sult of Problem 11; the argument is virtually the same as that for the concurrence of
the perpendicular bisectors of the sides of a triangle, Problem 20, Section 3.3.)
D
*This result is needed for Problem 14, Section 3.8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28a88382-6ec1-4393-ac86-3b4f05a3e53a%2Fd0cc036d-68f5-4287-8689-93d9379da036%2Fyhr9sfs.jpeg&w=3840&q=75)
Transcribed Image Text:182
CHAPTER 3 Foundations of Geometry 2
(b) Drag Cto such a position that ray BC lies exterior to LBAB', What happens to
the locus of D in this case? Is your knowledge of Euclidean geometry sufficient
for you to explain this behavior?
3.7 Quad
(a)
(b)
MLCBA = 32.64°
%3D
mZCBA = 11.95°
A
B
D.
10. Assume the usual definition for circles. Consider the concentric circles in the figure,
and show that if OA and OB are radii of the smaller of the two circles, and
LOAC =LOBD, then AC = BD.
11. Prove that if I is any point on the bisector BD of LABC, then I is an interior point
of the angle and is equidistant from its sides, and conversely.
*12. Prove that the angle bisectors of any triangle are concurrent at a point I, called the
incenter, that is equidistant from the three sides of the triangle. (Hint: Use the re-
sult of Problem 11; the argument is virtually the same as that for the concurrence of
the perpendicular bisectors of the sides of a triangle, Problem 20, Section 3.3.)
D
*This result is needed for Problem 14, Section 3.8.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning