*Let's construct a pedal
triangle. Let triangle ABC be any triangle. Draw the triangle
ABC and extend the each side using dotted lines.*

*Then take any point P in
the plane. Construct the perpendicular lines to the each side
of ABC on the point P.*

*ow, let's take the midpoints
of the each side of RST. Then draw a circle and merge the padal
point P on the circle.*

*Now find the triangle RST
by constructing the segments connecting three points R,S, and
T which are the points of intersection between the pependicular
lines and the extended sides of the triangle ABC.*

*Move the padal point P around
the green circle. Let's draw the trace of the midpoints of each
side of RST. Here we get three ellipse for the each midpoint by
moving the padal point P around the circle.*

*Let's investigete the patal
curves. Now construct the circumcircle of the triangle ABC. Then
move to the padal point on the curcumcircle. What are you expecting
in this case? Can we have the same trace of the midpoints?*