**Lets begin by showing the construction of
a pedal triangle for a given triangle.**

**If P is one of the vertices of the triangle,
the following occurs:**

**tha is the triangle collapses into a line
which is an altitude of the original triangle.**

**If P is on a side of the triangle the following
occurs:**

**that is if p is along one of the sides of
the triangle, it corresponds to the point of intersection with
the perpendicular from that side.**

**Lets look and see what happens if the pedal
point corresponds to the centroid of a triangle:**

**If the pedal point is the incenter of the
triangle then:**

**the pedal triangle becomes the the triangle
with a circumscribed circle that is inscribed in the origial triangle.**