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PEDAL TRIANGLE

by Derelle McFarland

Through the following diagrams I will construct the pedal triangle. I must begin with the antipedal triangle ABC. By definition the antipedal triangle A of a given triangle T is the triangle of which T is the pedal triangle. I'll begin with triangle ABC and pedal point P inside the triangle.

Now, I will construct segments from P perpendicular to sides AB, AC and BC. Then I will construct a triangle from these points.

This red triangle is the pedal triangle given point P because the vertices are the feet of the perpendiculars from P to the sides.
I will further investigate the pedal triangle by finding two more pedal triangles to point P by using the previous steps to find the red pedal triangle.

This is the blue pedal triangle. Now I will construct the third pedal triangle, a green one.

What do we notice from the first pedal triangle (red) and the second one (green)? They are similar. This theorem states that the nth pedal n-gon of any n-gon is similar to the original one.

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