Suppose that point P is some point in the Euclidean Plane and P is exterior to triangle ABC. A pedal triangle may be formed by constructing lines through point P which are perpendicular to each of the sides of triangle ABC, finding the points of intersection, and constructing a new triangle through these points.
It is sometimes necessary to extend the sides of the triangle in order to construct the lines perpendicular to the sides of triangle ABC. In the diagram above, the points of intersection are labeled F, G, and H. It is rather simple to use Geometer's Sketchpad to construct a triangle through these points of intersection (shown in blue).
Notice that because P was closer to triangle ABC (in pink) this time, the pedal triangle has become smaller.
In this case, all three vertices of pedal triangle PQR were located on various sides of triangle ABC. Moreover, pedal triangle PQR was contained in the interior of triangle ABC.
Again, the vertices of triangle RST are located on the sides of triangle ABC and the pedal triangle is located in the interior of triangle ABC.
As before, the vertices of triangle RST are located on the sides of triangle ABC.