In triangle ABC we will look at any
point P in the plane. Then
the perpendiculars to the sides of
ABC through point P were constructed. These intersections are
R,S,T. The dashed green lines are the perpendicular lines. Triangle
RST is called the Pedal Triangle for the pedal point P.
Next we look at point P outside the
Observe what happens when P is on a
vertex. The triangle RST becomes an altitude of triangle ABC.
Move point P outside triangle ABC until
all three vertices of RST are collinear. This is the Simson Line.
Anytime you try to put P on a side
of triangle ABC , P will lie on one of the vertices RST.
The are many more interesting things
to try with the Pedal Point and Pedal Triangle. I enjoyed this