I*f P is any point on the circumcircle of triangle ABC, the the feet of the perpendiculars from P to the sides of the triangle (possible extended) are colinear.*

Joshua DuMont

The pedal triangle is created by picking a point P and extending the sides of ΔABC into lines. Drop perpendicular lines from point P to the lines extended from the sides of ΔABC. The intersections R, S, T formed from this are the vertices of the pedal triangle.

If point P is placed on the circumcenter of the triangle then it appears triangle RST is degenerate (R, S, and T are colinear).

We used two facts in this proof that you may not be familiar with:

Thale's theorem and Cyclic quadrilaterals have opposite angles which are supplementary