This write up explores and proves some facts about acute triangle. Given triangle ABC. Construct the Orthocenter H. Let points D, E, and F be the feet of the perpendiculars from A, B, and C respectfully.
If you are interested in accessing the GSP file to explore for the obtuse case, click here to down load the file.
If you download the GSP file and animate, you will see that as the point A crosses the dotted lines, which mark the crossover from acute to obtuse, the condition stops to be true.