Inscribed Angle Theorem: Take 2!
The [color=#ff00ff][b]pink angle[/b][/color] is said to be an [color=#ff00ff][b]inscribed angle[/b][/color] within the circle below. [br]This [color=#ff00ff][b]inscribed angle[/b][/color] intercepts the [color=#1e84cc][b]thick blue arc[/b][/color] of the circle. [br]Because of this, this [color=#1e84cc][b]thick blue arc[/b][/color] is said to be the [color=#ff00ff][b]inscribed angle[/b][/color]'s [color=#1e84cc][b]intercepted arc[/b][/color]. [br][br]Notice how the [color=#1e84cc]blue central angle[/color] also intercepts this same [color=#1e84cc][b]thick blue arc[/b][/color]. [br][br][b]To start:[/b][br]1) Move [color=#1e84cc][b]point [i]D[/i][/b][/color] wherever you'd like.[br]2) Adjust the size of the [b][color=#1e84cc]thick blue intercepted arc[/color] [/b]by moving the other 2 [b][color=#1e84cc]blue points [/color][/b](if you wish.) [br]3) Click the checkbox to lock [color=#1e84cc][b]point [i]D[/i][/b][/color]. [br]4) Follow the interactive prompts that will appear in the applet. [br][br]Interact with the following applet for a few minutes. [br]Then, answer the questions that follow.
1.
How many [color=#ff00ff][b]pink inscribed angles[/b][/color] fill a [color=#1e84cc]central angle[/color] that intercepts the [color=#1e84cc][b]same arc[/b][/color]?
2.
How does the [color=#1e84cc]measure of an central angle[/color] (of a circle) compare with the [color=#1e84cc][b]measure of the arc it intercepts[/b][/color]?
3.
Given your responses to (1) and (2) above, how would you describe the [color=#ff00ff][b]measure of an inscribed angle [/b][/color](of a circle) with respect to the [color=#1e84cc][b]measure of its intercepted arc[/b][/color]?