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