By: Stephen Bismarck
The pedal triangle is the triangle
formed by the intersections of the perpendiculars from a given
point to each side of a given triangle. Let me show you a picture
of what I'm talking about.
The blue triangle ABC is the given
triangle point P is the given point and the red triangle DEF is
the pedal triangle.
Here is the GSP sketch if you'd like
to look at it for yourself or make a script from it.
When point P is located on one of the
vertices of the given vertices something happens to the pedal
As you can see the pedal triangle turns
into the altitude of triangle ABC
There is a great relationship between
the circumcircle and the pedal point P.
Here is the circumcircle with the original
Now went the pedal point merges onto
the circle it gets wierd
When the pedal point P is on the circumcircle
the pedal triangle is always a segment