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Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle


	Let ABC be an acute triangle with area . Extend the altitudes of ABC to meet the circumcircle at A', B', and C' corresponding to A, B, and C, respectively. Let the hexagon AC'BA'CB' have area . Then .


	Contributed by: Jay Warendorff

See Exercise 283(d) in R. A. Johnson, Advanced Euclidean Geometry, Mineola, NY: Dover, 2007 p. 179.

Altitude (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

Hexagon (Wolfram MathWorld)

Polygon Area (Wolfram MathWorld)

"Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AreaOfAHexagonFormedByTheVerticesAndAltitudeExtensionsOfATri/

Contributed by: Jay Warendorff

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