MathDB

3

Part of 2011 Indonesia MO

Problems(1)

A triangle formed from unusual perpendicular lines

Source: Indonesian Mathematics Olympiad 2011, Day 1, Problem 3

9/13/2011
Given an acute triangle ABCABC, let lal_a be the line passing AA and perpendicular to ABAB, lbl_b be the line passing BB and perpendicular to BCBC, and lcl_c be the line passing CC and perpendicular to CACA. Let DD be the intersection of lbl_b and lcl_c, EE be the intersection of lcl_c and lal_a, and FF be the intersection of lal_a and lbl_b. Prove that the area of the triangle DEFDEF is at least three times of the area of ABCABC.
geometrycircumcircletrigonometryinequalitiestrig identitiesLaw of SinesLaw of Cosines