Schwarz's Triangle Problem
by Richard Rusczyk, Pythagorean Pages Editor

Schwarz's Triangle Problem is to inscribe a triangle of minimum perimeter inside an acute triangle. The orange and red triangle inside ABC has the feet of the altitudes of ABC as vertices. Meanwhile, DEF is an arbitrary triangle inscribed in ABC. Play with the picture above - you can move the labeled points around. Compare the red line to the dark blue path.

The applet above was generated by JavaSketchpad, part of Geometer's Sketchpad. For more information on JavaSketchpad, click the box in the bottom right of the image above.

(The applet above may take a few moments to load.)