MathDB

2021.G4

Part of Cono Sur Shortlist - geometry

Problems(1)

max of [ADJE]/AJ^2 wanted, A-excircle related

Source: 2021 Cono Sur Shortlist G4 https://artofproblemsolving.com/community/c1088686_cono_sur_shortlist__geometry

10/31/2022
Let ABCABC be a triangle and Γ\Gamma the AA- exscribed circle whose center is JJ . Let DD and EE be the touchpoints of Γ\Gamma with the lines ABAB and ACAC, respectively. Let SS be the area of the quadrilateral ADJEADJE, Find the maximum value that SAJ2\frac{S}{AJ^2} has and when equality holds.
geometrygeometric inequalityexcircle