# G.GCI.2 Inscribed Angle Theorems: Take 3!

- Author:
- Dan Dale, Tim Brzezinski

**Students:**The directions for this activity can be found below the applet.

## 1.

Use the **Ray** tool to construct the following:
Ray with **endpoint B **that passes through

**Ray with**

*A*.**endpoint**that passes through

*B*

*C*.## 2.

This angle with **vertex B** you've just constructed is said to be an

**inscribed angle of the circle**. This

**inscribed angle**is said to intercept

*B***arc**. Use the

*AC***Angle**tool to find and display the measure of this inscribed angle.

## 3.

Use the **Ray** tool to construct the following:
Ray with **endpoint O **that passes through

**Ray with**

*A*.**endpoint**that passes through

*O*

*C*.## 4.

Recall that this angle you've just constructed in the previous step is called a **central angle **of the circle.
**How does the measure of this central angle compare with the ****measure of the blue arc** it intercepts?

## 5.

Use the **Angle** tool to find and display the measure of this central angle.

## 6.

**How does the measure of the inscribed angle compare with the measure of the central angle **that intercepts the **same arc**? (Feel free to move **points A** and

*around!)*

**C**## 7.

Click the **Show Other Point** checkbox to display another point (**point D**) on the

**pink arc**. Then create an inscribed angle with

**vertex**that intercepts

*D***arc**. Then measure this angle. What do you notice?

*AC*## 8.

What, overall, can you conclude from this investigation? Can you come up with 2 conclusions?