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min (AB + BC + CD + DA)/ (AC + BD) for tangential ABCD

Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade,finals p3

November 13, 2022
geometrytangential quadrilateralgeometric inequalitytangential

Problem Statement

Quadrilateral ABCDABCD is circumscribed around circle kk. Gind the smallest possible value of AB+BC+CD+DAAC+BD\frac{AB + BC + CD + DA}{AC + BD}, as well as all quadrilaterals with the above property where it is reached.