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