In the diagram below, [math]\angle BDC[/math] is an example of an [b]inscribed angle[/b], because it lies within [math]\odot A[/math] and its vertex lies on the circle. It corresponds to central [math]\angle BAC[/math] because they both intercept the same arc, [math]\text{\overset{\frown}{BC}}[/math]. [math][/math] [br](An [b]intercepted arc [/b]is an arc with endpoints on each side of the angle.) [br]

[b][br]PART A. [/b]In the circle below, [math]\angle F[/math], [math]\angle G[/math], and [math]\angle H[/math] are examples of inscribed angles. Notice that all three angles intercept the same arc [math]\text{\overset{\frown}{JK}}[/math]. Use the angle [icon]/images/ggb/toolbar/mode_angle.png[/icon] measurement tool to compare their measures. What do you notice?

[b]PART B. [/b]Construct [math]\odot Z[/math] with the [icon]/images/ggb/toolbar/mode_circle2.png[/icon] tool. Then, create the [b]central angle[/b] [math]\angle WZY[/math] and the [b]inscribed angle [math]\angle WXY[/math][/b] using the point [icon]/images/ggb/toolbar/mode_point.png[/icon] and segment [icon]/images/ggb/toolbar/mode_segment.png[/icon] tools. Compare the measures of these two angles. [br][br][i][b]Note: [/b]You can rename points by right clicking on them. [/i]