Circle Constructions_ Tutorial
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School
University of South Carolina *
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Course
A503
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by MegaStar111012
3/15/24, 11:57 PM
Lesson Activity: Inscribed Circle
https://f1.app.edmentum.com/courseware-delivery/ua/134717/45616346/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
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Lesson Activity
Inscribed Circle
This activity will help you meet these educational goals:
You will use geometry software to construct an inscribed circle of a triangle.
Directions
Read the instructions for this self-checked activity. Type in your response to each question
and check your answers. At the end of the activity, write a brief evaluation of your work.
Activity
Use GeoGebra to construct an inscribed circle by going to this activity . For help, watch these
short videos about using GeoGebra measurement tools , points, lines, and angles , and
circles .
Part A
Create a triangle
of your choice. Using GeoGebra tools, construct the angle bisectors of
and
. Mark the intersection point of the angle bisectors, and label it point D. What
does point D represent? Explain your reasoning.
Answer:
the intercircle of the triangle
Space used (includes formatting): 38 / 15000
Hide Sample Answer
3/15/24, 11:57 PM
Lesson Activity: Inscribed Circle
https://f1.app.edmentum.com/courseware-delivery/ua/134717/45616346/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
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The point at which the angle bisectors of the triangle meet is the incenter, which is also the
center of the inscribed circle of the triangle. So, point D is the incenter.
Part B
Create a line through point D, perpendicular to
. Mark the intersection of
and the
perpendicular line, and label it point E. What does
represent? Explain your reasoning.
Answer:
is the radius of the largest circle that will fit within triangle
Space used (includes formatting): 78 / 15000
Since point D is the center of the circle that will be inscribed, and the inscribed circle will
intersect
at point E, is tangent to the inscribed circle. Since
is perpendicular to
tangent
, is the radius of the largest circle that will fit within triangle .
Hide Sample Answer
Part C
With point D as the center, create a circle passing through point E. Measure the radius of the
inscribed circle. Would the radius be different if you used a line perpendicular to
instead
of
to create the circle? Explain your reasoning.
3/15/24, 11:57 PM
Lesson Activity: Inscribed Circle
https://f1.app.edmentum.com/courseware-delivery/ua/134717/45616346/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
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Answer:
no, the side of the triangle will be tsangdent to the insribed circle.
Space used (includes formatting): 77 / 15000
No, the result would be the same. Since the sides of the triangle will be tangent to the
inscribed circle, a perpendicular line from the center to any side of the triangle will give the
same radius.
Hide Sample Answer
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a
brief evaluation of your work below. Note what you learned and what challenged you.
Answer:
5 i did pretty good
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3/15/24, 11:57 PM
Lesson Activity: Inscribed Circle
https://f1.app.edmentum.com/courseware-delivery/ua/134717/45616346/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
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Space used (includes formatting): 26 / 15000