In the GeoGebra applet below: [br][br]1) Use the SEGMENT [icon]/images/ggb/toolbar/mode_segment.png[/icon] tool to construct segments [math]\overline{DC}[/math], [math]\overline{DB}[/math], [math]\overline{EC}[/math], and [math]\overline{EB}[/math]. [br][br]2) Use the ANGLE [icon]/images/ggb/toolbar/mode_angle.png[/icon] tool to measure and display the measure of [math]\angle D[/math] and [math]\angle E[/math] . [br][br]Then, answer the questions that appear below the applet.
Immediately select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] arrow. Then drag the angle measures to a place where you can see them clearly. What do you IMMEDIATELY NOTICE? Describe in detail in the space provided.
Now drag the [b][color=#1e84cc]BLUE DOT on the blue slider[/color][/b] to change the measure of the circle's[b][color=#1e84cc] blue central angle[/color][/b]. (You can also enter any angle measure you wish). [br][br]Each [b][color=#666666]gray angle[/color][/b] is said to be an [b][color=#666666]inscribed angle[/color][/b] of this circle. Note that each gray inscribed angle intercepts the same arc (of the circle) as the [b][color=#1e84cc]blue central angle[/color][/b]. [br][br]What do you notice about the [color=#666666][b]measures of the gray inscribed angles[/b][/color] with respect to the [color=#1e84cc][b]measure of this blue central angle[/b][/color]?