Pedal Triangles

 

Let triangle ABC be any triangle. Then if P is any point in the plane, construct perpendiculars to the sides of ABC (extended if necessary) locate three points R, S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P.

 

I first constructed a Pedal Triangle when P was in triangle ABC.

 

 


 

What if P is on a side of the triangle?

When P is on side AB the entire pedal triangle is within triangle ABC.

But, will this always be the case?

As we can see in this example the pedal triangle will not always be within triangle ABC when P is on one of the sides of the triangle.


 

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

Here we see the pedal triangle forms an altitude from point P in the base. We see that points S and T are the same as point P. Therefore, point P and point R form a line rather than a triangle.

 

Thus, we see that there are many different forms of pedal triangles depending on where point P lies.


 

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