**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.**