Directions:
1) Plot a point C on the green arc in the applet above.
2) Construct ray CA and ray CB.
3) Find and display the measure of angle BCA.
4) Now, drag point C along the green arc. What do you notice?
The measure of this angle always stays the same, regardless of where on the circular arc it is!
5) Is there truly a "best" place to sit on this circle in order to have the "best" viewing angle? Explain.
What do you think? See your answer to (4) above!
6) Now, construct ray OB and OA.
7) Find and display the measure of angle BOA.
8) In the applet above angle BCA is called an inscribed angle.
You already know that angle BOA is called a central angle.
Both this inscribed angle and central angle intercept the same arc!
9) Do you notice a relationship among the measure of angle BCA (inscribed angle) and the measure of angle BOA (central angle)? If so, describe.
Here's a hint (if you don't notice anything):
Try dividing the measure of the inscribed angle by the measure of the central angle. What do you get?
10) Does this relationship change if point C is moved to any location on the green arc?
Well....take a look back at your answer to (4) above!