Pedal Triangle


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.

Pedal Triangle



When point P is located on one of the vertices of the given vertices something happens to the pedal triangle

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 sketch

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