In the context of a [color=#38761d][b]SPHERE[/b][/color], [br][br]A [color=#1e84cc][b]GREAT CIRCLE[/b][/color] is defined to be a [b][color=#1e84cc]CIRCLE[/color][/b] that lies on the [b][color=#38761d]SURFACE OF THE SPHERE[/color][/b] and [b]LIES ON A PLANE that PASSES THROUGH THE CIRCLE's CENTER.[/b] In essence, the center of a [b][color=#1e84cc]GREAT CIRCLE[/color][/b] and the center of the [b][color=#38761d]sphere[/color][/b] are the same. [br][br]Consequently, a [b][color=#1e84cc]GREAT CIRCLE[/color][/b] also the largest possible circle one can draw on a [b][color=#38761d]sphere[/color][/b]. [br][br]In the applet below, the [b][color=#ff00ff]pink arc[/color][/b] and [b][color=#1e84cc]blue arc[/color][/b] make up a [b][color=#1e84cc]GREAT CIRCLE. [/color][/b] [br][br][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions below the applet. [/color][/b]

[b]Directions: [/b] [br][br]Move the [b]2 WHITE POINTS[/b] anywhere you'd like on the [b][color=#38761d]sphere[/color][/b]. The [b][color=#ff00ff]PINK ARC[/color][/b] is part of a [b][color=#1e84cc]GREAT CIRCLE[/color][/b] of this [color=#38761d][b]SPHERE[/b][/color]. You can move the [b][color=#bf9000]YELLOW POINT[/color][/b] anywhere you'd like as well. [br][br]Again, note that the [b][color=#bf9000]YELLOW ARC[/color][/b] is [b][color=#bf9000]NOT PART[/color][/b] of a great circle. [br][br]Slide the slider slowly and carefully observe what happens.

1) Open GeoGebra 3D app on your device. [br][br]2) Press the 3 horizontal bars (upper left corner). Select OPEN. [br][br]3) In the SEARCH TAB that appears, type [b]Gh58sVPx[/b][br] Note this string of characters can be found in the URL here. [br] Be sure to either copy & paste this code or type it just the way you see it here. [br][br]4) The slider named[b] j[/b] controls the entire animation. [br] Slider [b]k_1[/b] adjusts the opacity (shading) of the green sphere. [br] Slider [b]a[/b] adjusts the radius of the sphere.