# Circumcenter

- Author:
- William Gripentrog, Tim Brzezinski

Interact with this applet for a few minutes, then answer the questions that follow. Be sure to change the locations of the triangle's

**PINK VERTICES**before and after sliding the slider!**Questions:**1) What can you conclude about the 3 white points? How do you know this? 2) What is the measure of each

**gray angle**? How do you know this? 3) What vocabulary terms best describes each

**brown dotted line**? Why is this? 4) Describe

**the intersection**of these

**3 brown dotted lines**.

**How do they intersect?**5) Use the angle tool to now measure and display the measures of this triangle's 3 interior angles. For angle measures > 180 degrees, use the menu (upper right hand corner) to adjust this.

**Point C**is called the

**circumcenter**of the triangle. Drag the

**pink vertices**around to help you answer the new few questions. 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

**green circle**with respect to the triangle's

**pink vertices**? 10) What previously learned theorem easily implies that the distance from the

**circumcenter**to any

**vertex**is equal to the distance from the

**circumcenter**to any other

**vertex**?

**Questions:**1) What can you conclude about the 3 white points? How do you know this? 2) What is the measure of each

**gray angle**? How do you know this? 3) What vocabulary terms best describes each

**brown dotted line**? Why is this? 4) Describe

**the intersection**of these

**3 brown dotted lines**.

**How do they intersect?**5) Use the angle tool to now measure and display the measures of this triangle's 3 interior angles. For angle measures > 180 degrees, use the menu (upper right hand corner) to adjust this.

**Point C**is called the

**circumcenter**of the triangle. Drag the

**pink vertices**around to help you answer the new few questions. 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

**green circle**with respect to the triangle's

**pink vertices**? 10) What previously learned theorem easily implies that the distance from the

**circumcenter**to any

**vertex**is equal to the distance from the

**circumcenter**to any other

**vertex**?