Shown in the applet below are a triangle, its [color=#cc0000]circumcircle[/color], and its [color=#38761d]9-point circle[/color]. [color=#ff7700]Point O[/color] is the triangle's [color=#ff7700]orthocenter[/color]. [br]What special theorem about a triangle's [color=#ff7700]9-Point Circle[/color] is being dynamically illustrated below? [br]Note: Be sure to move the [color=#38761d][b]BIG GREEN POINT[/b][/color] around! Also be sure to move the triangle's [b]gray vertices [/b]anywhere you'd like!
[b][color=#000000]Theorem:[/color][/b][br]The [color=#38761d][b]9-Point Circle[/b][/color] of a triangle [color=#38761d][b]bisects[/b][/color] the segment connecting the triangle's [color=#ff7700][b]orthocenter [/b][/color]to [color=#cc0000][b]any point on its circumcircle[/b][/color]!