8. (a) An isosceles triangle T has two sides of length d and the included angle between these sides has size 0 (radians), say. Determine the area of T and the value of 0 for which T has the maximal area for a given value of d. (b) Let C be a circle of radius 1 and centre O. Let X, Y and Z be three distinct points on C. Determine the maximal possible area of the triangle XYZ assuming that it is right-angled. (c) Now let A, B and C be three distinct points on the circle C of radius 1 and suppose that the sides AB, AC and BC of the triangle ABC have lengths x, x and y respectively. Thus the angles ABC = AĈB = ß say. Let D be the point on C such that BD is a diameter of C. Show that the angle ADB : %3D and hence deduce that x = 2 sin B.
8. (a) An isosceles triangle T has two sides of length d and the included angle between these sides has size 0 (radians), say. Determine the area of T and the value of 0 for which T has the maximal area for a given value of d. (b) Let C be a circle of radius 1 and centre O. Let X, Y and Z be three distinct points on C. Determine the maximal possible area of the triangle XYZ assuming that it is right-angled. (c) Now let A, B and C be three distinct points on the circle C of radius 1 and suppose that the sides AB, AC and BC of the triangle ABC have lengths x, x and y respectively. Thus the angles ABC = AĈB = ß say. Let D be the point on C such that BD is a diameter of C. Show that the angle ADB : %3D and hence deduce that x = 2 sin B.
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
hi, can you help me with this whole question.
thank you
![8. (a) An isosceles triangle T has two sides of length d and the included angle between these
sides has size 0 (radians), say. Determine the area of T and the value of 0 for which T has
the maximal area for a given value of d.
(b) Let C be a circle of radius 1 and centre O. Let X, Y and Z be three distinct points on C.
Determine the maximal possible area of the triangle XY Z assuming that it is right-angled.
(c) Now let A, B and C be three distinct points on the circle C of radius 1 and suppose that
the sides AB, AC and BC of the triangle ABC have lengths x, x and y respectively. Thus
the angles ABC = AĈB = B say.
Let D be the point on C such that BD is a diameter of C. Show that the angle ADB = B
and hence deduce that x =
2 sin B.
(d) By using the sine rule, or otherwise, show that y/x
y2 /a? + 2? = 4.
= 2 cos B and hence deduce that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f0ee4d-c883-4e97-b05f-6fd93d8f479a%2F2e3a64a2-2447-4680-b5de-4a4d29e62aaf%2Fvpoakj_processed.png&w=3840&q=75)
Transcribed Image Text:8. (a) An isosceles triangle T has two sides of length d and the included angle between these
sides has size 0 (radians), say. Determine the area of T and the value of 0 for which T has
the maximal area for a given value of d.
(b) Let C be a circle of radius 1 and centre O. Let X, Y and Z be three distinct points on C.
Determine the maximal possible area of the triangle XY Z assuming that it is right-angled.
(c) Now let A, B and C be three distinct points on the circle C of radius 1 and suppose that
the sides AB, AC and BC of the triangle ABC have lengths x, x and y respectively. Thus
the angles ABC = AĈB = B say.
Let D be the point on C such that BD is a diameter of C. Show that the angle ADB = B
and hence deduce that x =
2 sin B.
(d) By using the sine rule, or otherwise, show that y/x
y2 /a? + 2? = 4.
= 2 cos B and hence deduce that
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 6 steps with 13 images
![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