### Orthic Triangle

(some authors refer to this triangle as the pedal
triangle)

The triangle joining the feet of the altitudes of a triangle
is called the orthic triangle.

As a point of interest the orthocenter (H)
of the original triangle is the incenter (I)
of the orthic triangle. It is also interesting to note that the triangle
with smallest perimeter that can be inscribed in an acute-angled triangle
ABC is the orthic triangle of traingle ABC. For an interesting discussion
of this statement click here.

For a proof of the statement that the orthocenter of the original triangle
is the incenter of the orthic triange click
here.

For a GSP sketch showing the behaviour of the orthic triangle click
here.

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