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Van Aubel's Theorem for Triangles

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BP
PB'
2.43
BC'
C'A
+
BA'
A'C
2.43
AP
PA'
1.24
AC'
C'B
+
AB'
B'C
1.24
CP
PC'
2.82
CA'
A'B
+
CB'
B'A
2.82
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.

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