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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 .


	Contributed by: Jay Warendorff After work by: Mehmet Sahin

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

Circumcircle (Wolfram MathWorld)

Excenter (Wolfram MathWorld)

Excentral Triangle (Wolfram MathWorld)

Excircles (Wolfram MathWorld)

Hexagon (Wolfram MathWorld)

Polygon Area (Wolfram MathWorld)

"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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