Materials:
Compass
Straight Edge
Two Pages with Two Congruent Triangles
One Half Page with One Triangle that is Congruent to the others

Page 1
Construct the Incenter and the Inscribed Circle on the top triangle.
Construct the Circumcenter and the Circumscribed Circle on the bottom triangle.

Page 2
Consrtruct the Centroid on the top triangle.
Construct the Orthocenter on the bottom triangle.
On each line segment between the Orthocenter and a vertices of the triangle construct the midpoint.
Make sure you are constructing the midpoint between the orthocenter and the vertex of each angle
NOT THE ORTHOCENTER TO SIDE!.
Label each of these points A1, A2, A3

Page 3 (the half page)
On this page you need to trace the following points from Page 1 and Page 2 and label them as listed.
Incenter (I)
Circumcenter (C)
Centroid (G)
Orthocenter (O)
Three Midpoints of the sides of the triangle (M1, M2, M3)
Three Feet of the Altitudes (F1, F2, F3)
The three midpoints you found on Page 2 (A1, A2, A3)

After copying the points you should notice that three of the points (I, C, G, or O) are collinear.
Draw the line segment that contain the three collinear points.
Find the midpoint of this line segment and label it (E).
Place your compass point on (E) and your pencil point on M1 and draw a circle.
If you did this correct the circle should go through all 9 points (M1, M2, M3. F1. F2, F3, A1, A2, A3)

If you want to see what it is supposed to look like do a "GOOGLE" search for "Nine Point Circle".

external image moz-screenshot-2.jpg