2. (12 pts) One of the neat things about circles is how we can use them to prove theorems that seemingly have absolutely nothing to do with circles. For instance, it is possible to prove the Pythagorean Theorem using circles, and it is very cool. To start the proof, take any right triangle ABC with right angle at C, with sides labeled as usual: A b C B α Now construct the circle with center B and radius BA: A b C C B a Prove that a2+ b² = c²! [Hint: you'll want to see a few chords... so, extend AC and BC. Then you'll see two chords (one is a diameter), and you're interested in segment lengths... browse through the theorems in the notes to see what might be useful to apply here.]
2. (12 pts) One of the neat things about circles is how we can use them to prove theorems that seemingly have absolutely nothing to do with circles. For instance, it is possible to prove the Pythagorean Theorem using circles, and it is very cool. To start the proof, take any right triangle ABC with right angle at C, with sides labeled as usual: A b C B α Now construct the circle with center B and radius BA: A b C C B a Prove that a2+ b² = c²! [Hint: you'll want to see a few chords... so, extend AC and BC. Then you'll see two chords (one is a diameter), and you're interested in segment lengths... browse through the theorems in the notes to see what might be useful to apply here.]
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter6: Equations
Section: Chapter Questions
Problem 3GP
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![2. (12 pts) One of the neat things about circles is how we can use them to prove theorems
that seemingly have absolutely nothing to do with circles. For instance, it is possible
to prove the Pythagorean Theorem using circles, and it is very cool. To start the proof,
take any right triangle ABC with right angle at C, with sides labeled as usual:
A
b
C
B
α
Now construct the circle with center B and radius BA:
A
b
C
C
B
a
Prove that a2+ b² = c²!
[Hint: you'll want to see a few chords... so, extend AC and BC. Then you'll see two
chords (one is a diameter), and you're interested in segment lengths... browse through
the theorems in the notes to see what might be useful to apply here.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322742eb-4a31-4e3c-832a-7268262542b0%2Fffb24b85-5a6d-4d25-bd58-79235cd1dcba%2Fkgi8pw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. (12 pts) One of the neat things about circles is how we can use them to prove theorems
that seemingly have absolutely nothing to do with circles. For instance, it is possible
to prove the Pythagorean Theorem using circles, and it is very cool. To start the proof,
take any right triangle ABC with right angle at C, with sides labeled as usual:
A
b
C
B
α
Now construct the circle with center B and radius BA:
A
b
C
C
B
a
Prove that a2+ b² = c²!
[Hint: you'll want to see a few chords... so, extend AC and BC. Then you'll see two
chords (one is a diameter), and you're interested in segment lengths... browse through
the theorems in the notes to see what might be useful to apply here.]
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