**What
is a Pedal Triangle?**

**Let
triangle ABC be any triangle. If P is any point in the plane,
then the triangle formed by constructing perpendiculars to the
sides of ABC is the pedal triangle for the point P. XYZ forms
the pedal triangle.**

**Let's
do some investigating.**

**1.
What if the pedal point P is the Centroid of triangle ABC? First
construct the Centroid point G.**

Notice the when point P is moved to point G the pedal triangle changes shape.

**2.
What if the pedal point P is the Incenter of triangle ABC? First,
construct the Incenter point I.**

**Notice
what happens when point P is moved to point I.**

**3.
What if the pedal point P is the Orthocenter of triangle ABC?
We will first construct the Orthocenter(H) of ABC. Notice that
the Orthocenter is outside ABC.**

**4. Let's adjust our
original triangle ABC so that the Orthocenter is inside the triangle.
Notice what happens to the pedal triangle.**

**What
if pedal point P is the Circumcenter of triangle ABC?**

**What
if the Circumcenter is located outside of triangle ABC?**

**What
if P is on a side of triangle ABC?**

**We
can see what happens when P is on the side of ABC. In this example
Y and P become the same point. This would be true for any side
of ABC.**

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

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