2A. Explore Angle Measures
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?