Some questions to think about

  1. How does Fagnano's problem collapse when we try to apply it to a triangle ABC in which the angle A is obtuse?


    2. (Use GSP to help you out.)
     
     

  2. Something a little more advanced:  In the figure below, UV and VW make equal angles with CA.  Deduce that the orthocenter of any triangle is the incenter of its orthic triangle.  (in other words, if ABC is a triangular billiard table, a ball hit in the direction of UV, will go round the triangle UVW indefinitely, that is, until it is stopped by friction.)


Submit your answers on paper to your teacher.

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