# G.GCI.2 Inscribed Angle Theorem: Take 2!

- Author:
- Dan Dale, Tim Brzezinski

- Topic:
- Angles

The

**pink angle**is said to be an**inscribed angle**within the circle below. This**inscribed angle**intercepts the**thick blue arc**of the circle. Because of this, this**thick blue arc**is said to be the**inscribed angle**'s**intercepted arc**. Notice how the blue central angle also intercepts this same**thick blue arc**.**To start:**1) Move**point**wherever you'd like. 2) Adjust the size of the*D***thick blue intercepted arc**by moving the other 2**blue points**(if you wish.) 3) Click the checkbox to lock**point**. 4) Follow the interactive prompts that will appear in the applet. Interact with the following applet for a few minutes. Then, answer the questions that follow.*D*## 1.

How many **pink inscribed angles** fill a central angle that intercepts the **same arc**?

## 2.

How does the measure of an central angle (of a circle) compare with the **measure of the arc it intercepts**?

## 3.

Given your responses to (1) and (2) above, how would you describe the **measure of an inscribed angle **(of a circle) with respect to the **measure of its intercepted arc**?