MathDB

6

Part of 2003 JBMO Shortlist

Problems(1)

inequality with areas defined by parallel to sides of ABC

Source: JBMO Shortlist 2003

10/12/2017
Parallels to the sides of a triangle passing through an interior point divide the inside of a triangle into 66 parts with the marked areas as in the figure. Show that aα+bβ+cγ≥32\frac{a}{\alpha}+\frac{b}{\beta}+\frac{c}{\gamma}\ge \frac{3}{2} https://cdn.artofproblemsolving.com/attachments/a/a/b0a85df58f2994b0975b654df0c342d8dc4d34.png
inequalitiesJBMOJBMO Shortlist