# Inscribed Angle Theorems: Take 3!

Topic:
Angles, Circle
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 A. Ray with endpoint B that passes through C.

## 2.

This angle with vertex B you've just constructed is said to be an inscribed angle of the circle. This inscribed angle B is said to intercept arc AC. Use the 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 A. Ray with endpoint O that passes through 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 C around!)

## 7.

Click the Show Other Point checkbox to display another point (point D) on the pink arc. Then create an inscribed angle with vertex D that intercepts arc AC. Then measure this angle. What do you notice?

## 8.

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