Recall that the measure of an arc of a circle is the same as the measure of its corresponding [color=#0a971e]central angle[/color]. (See applet.)[br]In this applet, the [color=#0a971e]central angle always remains a straight angle (180 degrees)[/color]. Thus, the [color=#0a971e]intercepted arc[/color] is a [color=#0a971e]semicircle[/color]. [br][br]Click on the [color=#b20ea8]pink checkbox[/color] to show the [color=#b20ea8]inscribed angle[/color]. Notice how the i[color=#b20ea8]nscribed angle[/color] and [color=#0a971e]central angle[/color] both intercept the same arc. [br][br]Use the inscribed angle theorem you've just learned (from http://tube.geogebra.org/m/1473237) to make a conjecture as to what the measure of the [color=#b20ea8]inscribed angle[/color] in this applet should be. Be sure to move points[color=#1551b5] B[/color], [color=#1551b5]C[/color], and the [color=#b20ea8]pink vertex of the inscribed angle[/color] around as well. (You can also change the radius of the circle if you wish.)[br][br]Complete the following corollary: [b]An [color=#b20ea8]inscribed angle[/color] that intercepts a [color=#0a971e]semicircle[/color] is always.....[/b]

Key directions and questions are in the description above the applet.