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]The [b][color=#3c78d8]central angle[/color][/b]and the [color=#ff00ff][b]inscribed angle[/b][/color] share the same [color=#0000ff][b]intercepted 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 [color=#1e84cc]blue points. [/color]Make sure the [br] intercepted arc is a minor arc[br]3) Click the checkbox to lock [color=#ff0000][b]point [i]D[/i][/b]. [/color][br]4) Follow the interactive prompts that will appear in the applet. [br][br]Reset the app and Interact with the following applet for a few minutes. [br]Then, answer the questions that follow.
How many [color=#ff00ff][b]pink inscribed angles[/b][/color] fill a [b][color=#1e84cc]central angle[/color] [/b]that intercepts the [color=#1e84cc][b]same arc[/b][/color]?
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]?
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]?