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

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 .

T

H

H=2T