Pedal Triangle? I thought we were riding bikes!
By Stephanie Britt
GSP for general Pedal Triangle
A pedal triangle is an arbitrary point within the plane of a triangle. We began our pedal triangle with point p outside Triangle ABC.
We see that the point p and Pedal triangle EFG that we have an obtuse triangle.
The display below shows that no matter where p occurs on the outside of the triangle that the triangle will remain and obtuse triangle.
This is a link to observe.
If point P is on the inside of the triangle our pedal triangle looks like
And if our point P is on the edge of the orginal triangle our Pedal triangle looks like
Let's explore the possibilities of similar triangle created by having the pedal p occur within the triangle.
Now we can see that the triangles appear to be similar but are they, but with a little investigation we see that it takes three pedal triangles to create similar triangles.
We can see that the third and smallest pedal triangle created from point P is similar to the original triangle.
Below is a link to use to test if this is true for all points p within the original triangle.
If we rotate point p about the incenter of the triangle we get an interesting pattern.
What can you create?