Assignment 9

by

Jackson Huckaby

A script tool to create a Pedal triangle can be found here.

2. What if pedal point P is the centroid of triangle ABC?

3.What is pedal point P is the incenter of triangle ABC?

4. 3.What is pedal point P is the Orthocenter of triangle ABC?

If the orthocenter is outside the triangle?

9. Find all conditions in which the three vertices of the Pedal Triangle are collinear. This line is called the Simpson Line.

By dragging our Pedal Point we can see that the Simson Line is formed where our Pedal Triangle collapses. This happens to always occur only when the pedal point lies on the circumcircle of triangle ABC.

In these screen shots we can observe that as the Pedal Point moves towards the center our Pedal Triangle collapses on itself, and then inverts.

For the brief moment when our triangle is degenerate we have a Simson Line.

You can find an animation of the Pedal Point on the circumcircle here.

By tracing the Simson line during this animation we can see the envelope of the line.