MathDB
TT2008 Junior A-Level - P3

Source:

September 4, 2010
ratioinequalitiesgeometry proposedgeometry

Problem Statement

In his triangle ABCABC Serge made some measurements and informed Ilias about the lengths of median ADAD and side ACAC. Based on these data Ilias proved the assertion: angle CABCAB is obtuse, while angle DABDAB is acute. Determine a ratio AD/ACAD/AC and prove Ilias' assertion (for any triangle with such a ratio).