Circumcenter & Circumcircle Action!

Interact with this applet for a few minutes, then answer the questions that follow. Be sure to change the locations of the triangle's VERTICES both BEFORE and AFTER sliding the slider! In addition, note the pink slider controls the measure of the interior angle with pink vertex (lower left).

1.

What can you conclude about the 3 smaller blue points? What are they? How do you know this?

2.

What vocabulary term best describes each brown line? Why is this?

3.

Describe the intersection of these 3 brown lines. How do they intersect?

The ORANGE POINTis called the CIRCUMCENTER of the triangle. Also, note that the pink slider controls the measure of the interior angle with pink vertex (lower left).

6.

Is it ever possible for the circumcenter to lie outside the triangle? If so, how would you classify such a triangle by its angles?

7.

Is it ever possible for the circumcenter to lie on the triangle itself? If so, how would you classify such a triangle by its angles? And if so, where exactly on the triangle is the circumcenter found?

8.

Is it ever possible for the circumcenter to lie inside the triangle? If so, how would you classify such a triangle by its angles?

9.

What is so special about the purple circle with respect to the triangle's vertices?

Quick (Silent) Demo

10.

What previously learned theorem easily implies that the distance from the circumcenter to any vertexis equal to the distance from the circumcenter to any other vertex?