[b][color=#980000]Note:[/color][/b][color=#000000] This applet immediately follows the investigation found [url=https://tube.geogebra.org/m/TJfdgdWb]here[/url][/color][color=#000000].[br] [/color][color=#000000]Directions appear below the applet. [/color]
[color=#980000][b]Directions: [/b][/color][br][br][color=#000000]1) Plot a [/color][color=#1e84cc][b]point [i]C[/i][/b][/color][color=#000000] on the [/color][color=#38761d][b]green arc[/b][/color][color=#000000] in the applet above. [br]2) Construct ray [i]CA[/i] and ray [i]CB. [br][/i]3) Find and display the measure of angle [i]BCA[/i]. [/color]
[color=#000000]4) Now, drag [/color][color=#1e84cc][b]point [i]C[/i] [/b][/color][color=#000000]along the [/color][color=#38761d][b]green arc[/b][/color][color=#000000]. What do you notice? [/color]
[color=#000000]The measure of this angle [b][i]always[/i] stays the same[/b], regardless of where on the circular arc it is! [/color]
[i][color=#9900ff]5) Is there truly a "best" place to sit on this circle in order to have the "best" viewing angle? Explain. [/color][/i]
[color=#000000]What do you think? [i]See your answer to (4) above! [/i][/color]
[color=#000000]6) Now, construct ray [i]OB[/i] and [i]OA[/i]. [br]7) Find and display the measure of angle [i]BOA[/i]. [br][br]8) In the applet above angle [i]BCA[/i] is called an inscribed angle. [br] You already know that angle [i]BOA[/i] is called a central angle. [br] Both this inscribed angle and central angle [b]intercept the same arc! [/b] [br][/color]
[color=#000000]9) Do you notice a relationship among the measure of angle [i]BCA [/i](inscribed angle) and the measure of angle [i]BOA[/i] (central angle)? If so, describe. [br][br][/color][color=#000000][br][/color]
[color=#000000]Here's a hint (if you don't notice anything): [br][i]Try dividing the measure of the inscribed angle by the measure of the central angle. What do you get? [/i][/color]
[color=#000000]10) Does this relationship change if [/color][color=#1e84cc][b]point C[/b][/color][color=#000000] is moved to any location on the [/color][color=#38761d][b]green arc[/b][/color][color=#000000]? [/color]
[color=#000000][i]Well....take a look back at your answer to (4) above! [/i][/color]