Van Aubel's Theorem for Triangles

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In a triangle ABC, draw lines from the vertices through a single point P in the interior of the triangle to points A', B' and C' on the opposite sides. This illustrates Van Aubel's Theorem:

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BP/PB' = BC'/C'A + BA'/A'C,

AP/PA' = AC'/C'B + AB'/B'C, and

CP/PC' = CA'/A'B + CB'/B'A.

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Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


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