[color=#000000]Interact with the applet below for a few minutes. Then answer the questions that follow. [br][br][/color][color=#0000ff]Be sure to change the locations of the[/color][color=#000000] [b]BIG POINTS[/b] [/color][color=#0000ff]each time [i]before[/i] you slide the slider. [/color]
Suppose the [color=#ff00ff][b]entire pink arc measures 200 degrees[/b][/color] and the [color=#1e84cc][b]entire blue arc measures 50 degrees[/b][/color]. [br][b][color=#bf9000]What would the measure of the manila angle be? [br][/color][/b]
[b][color=#ff00ff]Move ANY ONE (just ONE -- doesn't matter which) of the PINK POINTS[/color][/b] so the secant segment (for which this pink point is an endpoint) becomes TANGENT to the circle. [br][br]Answer question #1 again within THIS CONTEXT.
Now [color=#ff00ff][b]m[/b][b]ove the pink points[/b][/color] so that BOTH secant segments become TANGENT SEGMENTS.[br]Suppose, in this case, the entire pink arc measures 200 degrees. [br][br][b][color=#1e84cc]What would the measure of the blue arc be? [/color][/b][br][color=#bf9000][b]What would the measure of the manila angle be? [/b][/color]
Next, move the [b][color=#bf9000]MANILA POINT[/color][/b] (outside the circle) as close to the circle as possible so that the [b][color=#1e84cc]blue arc[/color][/b] almost disappears. (It won't disappear entirely). Keep the [b][color=#bf9000]MANILA POINT[/color][/b] on the circle. Now slowly re-slide the slider again. [br][br]What previously learned theorem do these transformations reveal? [br]
Suppose the 2 secant segments (drawn from the [b][color=#bf9000]manila point[/color][/b] outside the circle) intersect the circle above so that the [b][color=#bf9000]manila angle measures 60 degrees[/color][/b] and the [b][color=#ff00ff]entire pink arc measures 200 degrees[/color][/b]. If this is the case, [color=#1e84cc][b]what would the measure of the entire blue arc be[/b][/color]?