ABC is a equilateral triangle. P is a point inside the triangle.
Draw three line segments PD, PE, and PF perpendicular to
BC, CA, and AB respectively.
Prove PD+PE+PF is constant.
Applet
Drag the red point indside the triangle.
Check "Hint" check box. What the figure imply?
Click the "Hint" check box again.
Click "mode 2" check box. The point will be fixed on the side BC.