Copy of 9-Point Circle Action (Part 1)
For every triangle that exists, there is a very special circle that passes through 9 points. Some of these points lie on the triangle itself, and some do not.
The applet below will informally illustrate the construction of a triangle's 9-point circle.
Be sure to change the locations of the triangle's BIG WHITE VERTICES each time before re-sliding the slider. It would also be wise to alter the locations of these vertices after you've constructed this 9-point circle.
Take your time with this applet! Study its dynamics very carefully. Answer the questions that follow.
Questions:
1) Where exactly is the center of a triangle's 9-point circle located?
That is, how would you describe to somebody how to locate it?
Be sure to use appropriate vocabulary terms and be sure to be specific in your response!
The center of a triangles 9 point circle is located at the midpoint of the triangles orthocenter and circumcenter.
2) Describe the points that are located on a triangle's 9-point circle. What exactly are these points?
That is, how do these points relate to features of the triangle itself? The points that make up a 9 point circle are
- The triangles midpoints
- The points that meet at a triangles altitudes and segments
- The altitude's midpoints
- The points that meet at the triangles perpendicular bisectors and segments