Section 2: Circumcenter
Directions for Using the Applet:
- Change the triangle’s shape before and after sliding.
- Try making the triangle acute, right, and obtuse to see how things change.
- The 3 small blue points that appear on the triangle’s sides.
- The 3 brown lines connected to those points.
- Where the brown lines intersect (orange point = Circumcenter).
- The purple circle that appears around the triangle.
- The pink slider, which controls the angle at the pink vertex in the lower left.
Questions to Answer (Write in Complete Sentences):
1. What are the three small blue points on the triangle? How do you know?
2. What kind of lines are the three brown lines? What makes you say that?
3. What do you notice about the intersection of the three brown lines?
4. The orange point is the circumcenter. Based on what you observed: a) Can the circumcenter ever lie outside the triangle? If yes, what type of triangle causes this? b) Can the circumcenter lie on the triangle? If yes, what type of triangle causes this, and where is the circumcenter located? c) Can the circumcenter lie inside the triangle? If yes, what type of triangle causes this?
5. What do you notice about the purple circle and the triangle’s vertices?
6. What previously learned theorem explains why the distance from the circumcenter to each vertex is always the same?