Van Aubel's Theorem for Triangles

​
BP
PB
2.43
BC
CA
+
BA
AC
2.43
AP
PA
1.24
AC
CB
+
AB
BC
1.24
CP
PC
2.82
CA
AB
+
CB
BA
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.

External Links

Van Aubel's Theorem (Wolfram MathWorld)

Permanent Citation

Jay Warendorff
​
​"Van Aubel's Theorem for Triangles"​
​http://demonstrations.wolfram.com/VanAubelsTheoremForTriangles/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011