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The Excentral Triangle and a Related Hexagon

Let ABC be a triangle with excenters A', B', and C' opposite A, B, and C, respectively. Let A'', B'', and C'' be the circumcenters of A'BC, B'CA, and C'AB, respectively. Let be the area of A'B'C' and be the area of the hexagon AB''CA''BC''. Then .

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See problem J95 in "Problem Column," Mathematical Reflections [online], 4, 2008 p. 1.

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"The Excentral Triangle and a Related Hexagon" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/TheExcentralTriangleAndARelatedHexagon/
Contributed by: Jay Warendorff
After work by: Mehmet Sahin




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