Centers of Triangles Exploration

Below is a triangle RST, with its centroid (G), circumcenter (C), incenter (I), and orthocenter (O) constructed. The top vertex T of the triangle is locked on line AB. Drag that vertex along the line and watch as each of the centers traces its path across the screen. You can turn the traces off and on by right clicking the points and selecting "Trace On" from the menu.

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Questions to think about:
Which centers traced straight lines? Was there anything special about the lines?
Which centers traced curved lines? Was there anything special about the curves?
How does the centroid's path relate to line AB? Why would that happen?
How does the circumcenter's path relate to line RS? Why would that happen?
How does the incenter's path relate to the points R and S? Why would that happen?
How does the orthocenter's path relate to the points R and S? Why would that happen?

Brian Bisignani, June 26, 2008, Created with GeoGebra