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Areas of Two Triangles

Source: 2012 Baltic Way, Problem 13

November 22, 2012
geometrycircumcircletrigonometryinequalitiesgeometry unsolved

Problem Statement

Let ABCABC be an acute triangle, and let HH be its orthocentre. Denote by HAH_A, HBH_B, and HCH_C the second intersection of the circumcircle with the altitudes from AA, BB, and CC respectively. Prove that the area of triangle HAHBHCH_A H_B H_C does not exceed the area of triangle ABCABC.
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