Trisected perimeter point

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The trisected perimeter point of a 3-4-5 right triangle. For this triangle, C´B = A´C and BA´ = CB´, but that is not the case for triangles of other shapes.

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 X₃₆₉ in Clark Kimberling's Encyclopedia of Triangle Centers. Uniqueness and a formula for the trilinear coordinates of X₃₆₉ were derived by Peter Yff.

[edit] References

• Kimberling, C. Encyclopedia of Triangle Centers. X(369) = 1st TRISECTED PERIMETER POINT.

[edit] External links

• Eric W. Weisstein, Trisected Perimeter Point at MathWorld.

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