[color=#000000]For every triangle that exists, there is a[/color] [color=#1e84cc][b]very special circle[/b][/color] that passes through [color=#ff00ff][b]9 points[/b][/color]. [color=#000000]Some of these [/color][color=#ff00ff][b]points[/b][/color][color=#000000] lie on the triangle itself, and some do not. [/color][br][br][color=#000000]The applet below will informally illustrate the construction of a triangle's[/color] [color=#1e84cc][b]9-point circle[/b][/color][color=#000000]. [br]Be sure to change the locations of the triangle's[/color][b] BIG WHITE VERTICES[/b][color=#000000] each time before re-sliding the slider. It would also be wise to alter the locations of these [/color][b]vertices[/b][color=#000000] [b][i]after[/i][/b] you've constructed this [/color][color=#ff00ff][b]9-point circle[/b][/color][color=#000000]. [/color]