Van Aubel's Theorem for Triangles

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:

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.