# G.GCI.3 Circumcenter & Circumcircle Action!

- Author:
- Dan Dale, Tim Brzezinski

**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 POINT**is 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?