Trisected perimeter point
- Trisected perimeter point
In geometry, given a triangle "ABC", there exist unique points "A´", "B´", and "C´" on the sides "BC", "CA", "AB" respectively, such that:
:* "A´", "B´", and "C´" partition the perimeter of the triangle into three equal-length pieces. That is, "C´B" + "BA´" = "B´A" + "AC´" = "A´C" + "CB´".
:* The three lines "AA´", "BB´", and "CC´" meet in a point, the trisected perimeter point.
This is point "X"369 in Clark Kimberling's "Encyclopedia of Triangle Centers". Uniqueness and a formula for the trilinear coordinates of "X"369 were derived by Peter Yff.
References
*Kimberling, C. "Encyclopedia of Triangle Centers". [http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X369 X(369) = 1st TRISECTED PERIMETER POINT] .
External links
*mathworld|urlname=TrisectedPerimeterPoint|title=Trisected Perimeter Point
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