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
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