Where to Sit?

Topic:
Angles, Circle
Note: This applet immediately follows the investigation found here. Directions appear below the applet.
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?

5) Is there truly a "best" place to sit on this circle in order to have the "best" viewing angle? Explain.

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.

10) Does this relationship change if point C is moved to any location on the green arc?