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Pedal Triangle

By

B.J Kim

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

 

When P is the centroid , then the pedal triangle is inside the triangle. Because the centroid is always inside the triangle, it make sense that the pedal triangle will also stay inside the triangle.

3. What if...P is the incenter...?

If P is the incenter, then the pedal triangle is inside the triangle and P becomes the circumcenter of the pedal triangle.

 

4. What if...P is the Orthocenter...? Even if outside ABC?

If P is the orthocenter then the pedal triange becomes the Orthic Triangle.

 

5. What if...P is the Circumcenter...? Even if outside ABC?

If P is the circumcenter, then the pedal triangle becomes the Medial Triangle. Each side of the pedal triangle represents the medsegments of the original despite when P is in side or outside the triangle.

 

7. What if P is on a side of the triangle?

If P is on the side of the triangle, then P becomes a vertice of the pedal triangle. Despite the type of triangle, two vertices of the pedal triangle will always lie on the original triangle.(extended if necessary)

 

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

If P is one of the vertices, then the pedal triangle becomes the altitude of the triangle. This makes sense the pedal triangle is constructed by perpendiculars of the sides of the original triangle and the altitude is the perpendicular to a side from a vertice. As you can see in an obtuse triangle the pedal triangle/altitude is outside of the triangle. In the acute triangle it is inside the triangle.