[color=#cc0000][b]Students:[/b][/color][br]The directions for this activity can be found below the applet.
Use the [b]Ray[/b] tool to construct the following: [br][br]Ray with [color=#666666][b]endpoint [i]B[/i] [/b][/color]that passes through [b][color=#1e84cc][i]A[/i].[/color][/b][br]Ray with [color=#666666][b]endpoint [i]B[/i] [/b][/color]that passes through [color=#1e84cc][b][i]C[/i].[/b][/color]
This angle with [color=#666666][b]vertex [i]B[/i][/b][/color] you've just constructed is said to be an [b]inscribed angle of the circle[/b]. [br]This [b]inscribed angle [i]B[/i][/b] is said to intercept [color=#1e84cc][b]arc [i]AC[/i][/b][/color]. [br][br]Use the [b]Angle [/b]tool to find and display the measure of this inscribed angle.
Use the [b]Ray[/b] tool to construct the following: [br][br]Ray with [color=#666666][b]endpoint [i]O[/i] [/b][/color]that passes through [b][color=#1e84cc][i]A[/i].[/color][/b][br]Ray with [color=#666666][b]endpoint [i]O[/i] [/b][/color]that passes through [color=#1e84cc][b][i]C[/i].[/b][/color]
Recall that this angle you've just constructed in the previous step is called a [b]central angle [/b]of the circle. [br][b]How does the measure of this central angle compare with the [/b][color=#1e84cc][b]measure of the blue arc[/b][/color] it intercepts? [br][br]Use the [b]Angle[/b] tool to find and display the measure of this central angle.
[b]How does the measure of the inscribed angle compare with the measure of the central angle [/b]that intercepts the [color=#1e84cc][b]same arc[/b][/color]? (Feel free to move [color=#1e84cc][b]points [i]A[/i][/b][/color] and [i][color=#1e84cc][b]C[/b][/color][/i] around!)
Click the [b]Show Other Point[/b] checkbox to display another point ([color=#666666][b]point [i]D[/i][/b][/color]) on the [color=#ff00ff][b]pink arc[/b][/color]. [br]Then create an inscribed angle with [color=#666666][b]vertex [i]D[/i][/b][/color] that intercepts [color=#1e84cc][b]arc [i]AC[/i][/b][/color]. [br]Then measure this angle. [br]What do you notice?
Complete the following statements: [br][br][i]A central angle is[/i]_______________the measure of the intercepted arc.[br][br][br] [br][i]An Inscribed Angle is [/i]_________________the measure of its intercepted arc. [br]