1. [b]Explore the triangle in the applet[/b] by clicking and dragging the [b]WHITE VERTICES[/b] of the triangle to new positions.[br][br]2. Use the [b]slider[/b] to adjust the construction. Make sure to:[br][list][*]Change the triangle’s shape [b]before[/b] and [b]after[/b] sliding.[/*][*]Try making the triangle acute, right, and obtuse to see how things change.[br][/*][/list][br]3. Pay attention to:[br][list][*]The [b]3 small blue points[/b] that appear on the triangle’s sides.[/*][*]The [b]3 brown lines[/b] connected to those points.[/*][*]Where the brown lines intersect (orange point = [b]Circumcenter[/b]).[/*][*]The [b]purple circle[/b] that appears around the triangle.[/*][*]The [b]pink slider[/b], which controls the angle at the pink vertex in the lower left.[br][/*][/list][br]4.[b] Interact with the applet for a few minutes.[/b][br]Try different triangle shapes and adjust the sliders. Observe how the circumcenter and the circle behave.[br][br]5. If you’re unsure what to do, scroll to the bottom and watch the [b]“Quick (Silent) Demo.”[/b]
1. What are the [b]three small blue points[/b] on the triangle? How do you know?
2. What kind of lines are the [b]three brown lines[/b]? What makes you say that?
3. What do you notice about the [b]intersection of the three brown lines[/b]?
4. The [b]orange point[/b] is the [b]circumcenter[/b]. Based on what you observed:[br][br]a) Can the circumcenter ever lie [b]outside[/b] the triangle? If yes, what type of triangle causes this?[br][br]b) Can the circumcenter lie [b]on[/b] the triangle? If yes, what type of triangle causes this, and where is the circumcenter located?[br][br]c) Can the circumcenter lie [b]inside[/b] the triangle? If yes, what type of triangle causes this?
5. What do you notice about the [b]purple circle[/b] and the triangle’s vertices?
6. What [b]previously learned theorem[/b] explains why the distance from the circumcenter to each vertex is always the same?