Honors Geometry
Date: ________________
Name ____________________________
/ 35 points
Objective: To construct a nine-point circle using Geometer’s Sketchpad and to investigate
it’s special properties.
Introduction: There are several steps to this project beginning
with the construction of a nine-point circle using GSP. You will
then conduct a little research on the history behind the 9-point
circle and discover and interpret some of the properties of this
very interesting geometric figure. The GSP file should be
emailed to Mrs. Doherty by the start of the class period on
Wed. 12/18/13. The Web Quest part should be printed and
handed in by the same date.
Part I: Construction of the 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 . These are the first three of the nine points.
3. Construct the altitudes of the . Then construct the points of intersection of the sides
and the altitudes. These are 3 more of the points.
4. Construct the intersection of the altitudes.
5. Now find midpoints of the segments formed from this point to each vertex. These are
the final three points.
6. We now have the nine points!
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
points.
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.
To hide lines, select the line and then command-h.
MCD/12-13
1
Honors Geometry
Date: ________________
Name ____________________________
Part II: Web Quest (20 points)
Research the answers to the following questions on the Internet.
Type your answers into the document, print and submit the hard
copy by 12/18.
1. What are the intersections of the following segments known as:
a. Altitudes______________________________
Leonhard Euler:
Famous mathematician
or pastry chef? (J.K!)
b.  Bisectors _____________________________
c. Medians _______________________________
d.  Bisectors ____________________________
2. The intersection of the  Bisectors of a ∆ are equidistant from the vertices of the ∆,
therefore it is also equidistant from what else? Explain your answer.
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?
4. What is the center of gravity of a triangle and where does it occur?
5. What is the relationship of the location of the centroid with respect to the vertices of
a triangle?
6. Of the four intersections of segments from question 1, what are the possible locations
of these intersections with respect to the ∆? Be specific!
7. List 3 properties of the 9-point circle not already discussed.
8. In a single paragraph, provide a brief history of Leonhard Euler, Euler’s line and provide
2 facts regarding Euler’s line not already discussed.
MCD/12-13
2