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School
University of South Carolina *
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Course
B221
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by DeanFireBoar49
3/17/24, 1
:
21 PM
Lesson Activity: Inscribed Circle
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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 point at which the angle bisectors of the triangle meet is the incenter. So, point D is the
incenter. Space used (includes formatting): 143 / 15000
3/17/24, 1
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Lesson Activity: Inscribed Circle
Page 2 of 4
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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.
Hide Sample Answer
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:
Since point D is the center of the circle that will be inscribed, and the inscribed circle will intersect
AB at point E, AB is tangent to the inscribed circle. Since DE is perpendicular to tangent AB, DE is
the radius of the largest circle that will fit within triangle ABC.
Space used (includes formatting): 309 / 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
3/17/24, 1
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Lesson Activity: Inscribed Circle
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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.
Answer:
The radius would be the same, whether the circle is constructed with a line perpendicular to AB or
AC, as long as D remains the center and E remains a point on the circle.
Space used (includes formatting): 183 / 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.
Your preview ends here
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3/17/24, 1
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21 PM
Lesson Activity: Inscribed Circle
Page 4 of 4
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Answer:
4 i feel as if i did pretty well
Space used (includes formatting): 51 / 15000