Inscribed Angle Theorem

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. The central angleand the inscribed angle share the same intercepted arc To start: 1) Move point D wherever you'd like. 2) Adjust the size of the thick blue intercepted arc by moving the other 2 blue points. Make sure the intercepted arc is a minor arc 3) Click the checkbox to lock point D. 4) Follow the interactive prompts that will appear in the applet. Reset the app and Interact with the following applet for a few minutes. Then, answer the questions that follow.


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


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



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?