Investigation: Select two pedal points on the circumcircle and construct their Simpson lines. Compare the angle of intersection of the two Simpson lines with the angular measure of the arc between the two pedal points.

We begin by constructing the situation to be investigated in Geometer's Sketchpad. Additionally, we measure the angular measure of the arc between the two pedal points as well as two angles of intersection to consider.

CONJECTURE: The measurement of the acute angle of intersection of the Simpson lines of two pedal points on the circumcircle of triangle ABC is half the angular measure of the arc between the two pedal points. To try it yourself, click here.