Pedal Triangles

Let triangle ABC be any triangle. Then if P is any point in the plane,
construct perpendiculars to the sides of ABC (extended if necessary) locate
three points R, S, and T that are the intersections. Triangle RST is the ** Pedal
Triangle **for

I first constructed a Pedal
Triangle when P was in triangle ABC.

What if P is on a side of
the triangle?

When P is on side AB the
entire pedal triangle is within triangle ABC.

But, will this always be
the case?

As we can see in this
example the pedal triangle will not always be within triangle ABC when P is on
one of the sides of the triangle.

What if P is one of the
vertices of triangle ABC?

Here we see the pedal
triangle forms an altitude from point P in the base. We see that points S and T
are the same as point P. Therefore, point P and point R form a line rather than
a triangle.

Thus, we see that there are
many different forms of pedal triangles depending on where point P lies.