MathDB

13

Part of 2012 Baltic Way

Problems(1)

Areas of Two Triangles

Source: 2012 Baltic Way, Problem 13

11/22/2012
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.
geometrycircumcircletrigonometryinequalitiesgeometry unsolved