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Points of Concurrency
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1. Circumcenter
- Circumcenter & Circumcircle Action!
- Circumcenter Construction
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2. Incenter
- Incenter + Incircle Action (V2)!
- G.GCI.3 Constructing an Incenter: Ex. 11
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Points of Concurrency
linzi_bullard, Jan 23, 2024
Points of Concurrency
Table of Contents
- Circumcenter
- Circumcenter & Circumcircle Action!
- Circumcenter Construction
- Incenter
- Incenter + Incircle Action (V2)!
- G.GCI.3 Constructing an Incenter: Ex. 11
Circumcenter & Circumcircle Action!
Interact with this applet for a few minutes, then answer the questions that follow.
Be sure to change the locations of the triangle's VERTICES both BEFORE and AFTER sliding the slider!
In addition, note the pink slider controls the measure of the interior angle with pink vertex (lower left).
1.
What can you conclude about the 3 smaller blue points? What are they? How do you know this?
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2.
What vocabulary term best describes each brown line? Why is this?
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3.
Describe the intersection of these 3 brown lines. How do they intersect?
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The ORANGE POINTis called the CIRCUMCENTER of the triangle.
Also, note that the pink slider controls the measure of the interior angle with pink vertex (lower left).
6.
Is it ever possible for the circumcenter to lie outside the triangle?
If so, how would you classify such a triangle by its angles?
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7.
Is it ever possible for the circumcenter to lie on the triangle itself?
If so, how would you classify such a triangle by its angles?
And if so, where exactly on the triangle is the circumcenter found?
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8.
Is it ever possible for the circumcenter to lie inside the triangle?
If so, how would you classify such a triangle by its angles?
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9.
What is so special about the purple circle with respect to the triangle's vertices?
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10.
What previously learned theorem easily implies that the distance from the circumcenter to any vertexis equal to the distance from the circumcenter to any other vertex?
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For a hint, click here.
Incenter + Incircle Action (V2)!
In the app below, you can change the size of the triangle by moving any one (or more) of its vertices.
You can also alter the size of the angle in the lower left corner by using the smaller slider.
(You can also zoom in/out.)
1.
What vocabulary term would you use to describe the segments that have this triangle's vertices as its endpoints? Why?
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2.
How do these 3 segments intersect? Describe.
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3.
The point you see inside the triangle is called the INCENTER of this triangle.
Notice there are 3 equal distances in this triangle. How would you describe these equal distances in your own words?
That is, each of these distances is the distance from the _________ to ___________?
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4.
Why do your observation(s) and response to (3) above hold true? What previously learned theorem justifies this?
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For a hint, click here.
Quick (Silent) Demo
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