The Excentral Triangle and a Related Hexagon

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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 .

Contributed by: Jay Warendorff (August 2008)
After work by: Mehmet Sahin
Open content licensed under CC BY-NC-SA


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Details

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



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