[color=#000000]Note: This worksheet follows the 9-Point Circle Action (Part 2) worksheet, which can be found here: https://tube.geogebra.org/m/EHpRBpFE[br][br]The applet below contains a triangle shown with its [/color][color=#38761d]9-Point Circle[/color][color=#000000] and [/color][color=#980000]circumcircle[/color][color=#000000]. The [/color][color=#ff00ff]pink vertices[/color][color=#000000] of the triangle are moveable, as well as the BIG WHITE POINT on its [/color][color=#980000]circumcircle[/color][color=#000000]. [br][/color][br][b][color=#000000]Directions: [/color][/b][br][br][color=#000000]1) Select the [b]Midpoint[/b] tool in the toolbar. Then select the [/color][color=#ff7700]orthocenter[/color][color=#000000] and the BIG WHITE POINT. [br] This will plot the [/color][color=#ff0000]midpoint[/color][color=#000000] of the path (segment) that connects the triangle's [/color][color=#ff7700]orthocenter [/color][color=#000000]to this BIG [br] WHITE POINT on its [/color][color=#980000]circumcircle. [br][br][/color][color=#000000]2) What do you notice? [br][br]3) Now, drag the WHITE POINT around the [/color][color=#980000]circumcircle[/color][color=#000000]. What do you notice about the [/color][color=#ff0000]midpoint[/color][color=#000000] of the path (segment) that connects the triangle's [/color][color=#ff7700]orthocenter [/color][color=#000000]to this BIG WHITE POINT on its [/color][color=#980000]circumcircle[/color][color=#000000]? [br][br][/color][color=#000000]4) Given your results for (2) & (3) we can say that triangle's [/color][color=#38761d]9-Point Circle[/color][color=#000000] is a __________________ of the segment that connects the triangle's [/color][color=#ff7700]orthocenter [/color][color=#000000]to [i]any point[/i] on its [/color][color=#980000]circumcircle[/color][color=#000000]. [br][br][/color][color=#1e84cc][i]Note: Feel free to use the segment and/or distance tools to further verify your answers to these [br] questions listed above. [/i][br][/color]