Name ________________________________________ Honors I
The use of Geometer’s Sketchpad to investigate the 9-point Circle
/ 45 pts
This project will be multi-step and also multi-purpose. You will be asked to construct a
nine point circle, research some history of it, and discover and interpret some of the
properties of this very interesting geometric figure. This will be a major grade of the first
marking period. The project must be emailed to Mr. Wieland by the beginning of your
class period on Friday November 4th.
Construction of 9 Point Circle
( 15 points)
The construction steps are listed below along with some of the terms involved.
1. Construct an acute , make it large enough to work with.
2. Find the midpoints of each side of the . There’s the first 3 points
3. Construct the altitudes of the , construct the point of intersections of the sides and
the altitudes. These are 3 of the points.
4. Now construct the intersection of the altitudes.
5. Now find midpoints of the segments formed from this point to each vertex. That’s 3
more points
6. We now have the nine points. (SEE THEM??)
7. Form a triangle using the midpoints of segments drawn in step 5.
8. Construct the  bisectors of each one of these segments and find their intersection.
9. Construct a circle with the intersection as the center of the circle going through the 9
pts.
10. Repeat the process with the  bisectors of the larger .
11. Construct a segment connecting the intersection of the altitudes of the larger  and
the  bisectors of the larger . (This is Euler’s Line)
NOTE*** Don’t forget that you can hide lines not needed to clean up the picture.
I will definitely be available for extra help, you may want to get together as a class before
or after school from time to time to check on progress.
Web Quest Part of Project ( 30 points)
You need to search the internet to discover properties , answer the specific questions and
analyze your findings and thoughts.
Questions that need to be answered:
1. What are the intersections of the following segments known as:
a. Altitudes______________________________
b.  Bisectors _____________________________
c. Medians _______________________________
d.  Bisectors ____________________________
2. The intersection of the  Bisectors of a ∆ are equidistance from the vertices of the
∆, therefore it is also equidistant from what else? (justify your answers)
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3. What appears to be true about the intersections of the  bisectors of both ∆’s and
the intersection of the altitude of the larger triangle?
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4. What is the center of gravity of a triangle and where does it occur?
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5. What is the relationship of the location of the centroid with respect to the vertices
of a triangle?
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6. Of the four intersections of segments from question 1, what is the possible
locations of them with respect to the ∆? Be specific
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7. Tell us 3 not discussed properties of the 9 point circle that you have found out due
to the research you have done.
a. ________________________________________________________________
b. ________________________________________________________________
c. ________________________________________________________________
8. Provide 2 facts not discussed regarding Euler’s line.
a. ____________________________________________________________
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b. ____________________________________________________________
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9. Provide a brief history of Euler and Euler’s line.