Orthic triangle of a triangle
Orthoptic triangle - a path of light
A triangle ABC is given. Draw the altitudes AD, BE,CF. The triangle DEF is called the orthic triangle of the triangle ABC.
It is the only path of light trapped in the triangle ABC, or equivalently the only closed triangular path in a triangular billiard. Check the incident angle and the reflected angle at each of the points D,E,F.
Modify the triangle ABC to check invariance of this property.
Reference:
Th. Dana-Picard and A. Haenel (1998): Triangles, polygons and beams of light, International Journal of Mathematical Education in Science and Technology 29 (6), 922-929.