Assignment #9

Pushing the
Pedal to the Limit!

P is the pedal point
of triangle ABC.

RST is the pedal
triangle for pedal point P.

## When the pedal point is on a side of the triangle ABC, the pedal triangle
becomes an obtuse triangle. As the
pedal point P approaches any vertex of the triangle, the obtuse angle of the
pedal triangle becomes more obtuse. The
limit as a pedal point approaches a vertex of the original triangle is a line
segment. This limit is called the
Simson line.

*Another interesting observation regarding the pedal
point is that once the three perpendiculars have passed through any two
vertices of the triangle ABC, the pedal triangle disappears. *

### PEDAGOGY

Pedal points are not
traditionally taught in secondary geometry, even at the honors or gifted level,
but some of the properties are very applicable particularly to honors and
gifted students because some of these ideas and concepts are good introductions
to higher level thinking that will be required in calculus.

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