MathDB
2019 Taiwan APMO Preliminary P3

Source: 2019 Taiwan APMO Preliminary

August 23, 2020
triangle inequalityGeometry inequalityalgebra

Problem Statement

Let △ABC\triangle ABC be an acute triangle, HH is its orthocenter. AH→,BH→,CH→\overrightarrow{AH},\overrightarrow{BH},\overrightarrow{CH} intersect △ABC\triangle ABC's circumcircle at A′,B′,C′A',B',C' respectively. Find the range (minimum value and the maximum upper bound) of AHAA′+BHBB′+CHCC′\dfrac{AH}{AA'}+\dfrac{BH}{BB'}+\dfrac{CH}{CC'}
Back to ProblemsView on AoPS